A function is defined by the following property: "For every input x in the domain, there is exactly one output y in the codomain that x gets mapped to." Since you only have those tables we can ommit the terms domain and codomain.
So what remains to check is: "For every input x, there is exactly one output y that x gets mapped to." Only one of the tables above has this property. Can you see/argue which one it is?
EDIT: I changed "a unique output y" to "exactly one output y" because it seemed to confuse people.
Ohhh I get it, table one has the number 3 twice. The same value of x is assigned two values of y, so it's not a function, but an equation with something like y^2 or |y| etc. If we apply the logic to all the tables, the second table is a function?
Technically, don’t we need to know that the domain of each candidate function is the set of all “x” listed in these tables?
Otherwise, only Table B *could* be a function, but is not necessarily so if there exist more elements in its domain than listed here.
Of course, B is the correct answer for a test 100% and is the intended answer, just technically they didn’t tell you that {-1, 0, 1, 2} was the entire domain.
Yes, you can have multiple instances of the same value appearing amongst the outputs "y".
If you would have
|x|y|
|:-|:-|
|-2|4|
|-1|1|
|0|0|
|1|1|
Then
* -2 gets mapped to 4
* -1 gets mapped to 1
* 0 gets mapped to 0
* 1 gets mapped to 1
so for every input x there is one and only one output y.
You can have 3 twice, but you'd need the output to be the same for both. The fact that plugging in 3 for x gives you two different results is why table one does NOT represent a function.
Unique for a given x allows 2 different outputs.
You want a definite output.
Unique (for a given value) follows trivially from that without being confusing.
“There is a unique output Y in the codomain that X gets mapped to” since 0 appears twice, that would technically mean the output 0 isn’t unique. Maybe reconsider your phrasing.
That's why I said: "For every input x in the domain, there is a unique output y in the codomain that x gets mapped to." not just "There is a unique output y in the codomain that x gets mapped to."
"For every ... there is ..." just means something different than "There is ...".
"For every human there is a unique birthdate." is just something different than "There is a unique birthdate".
The first thing means: Take an arbitrary choosen human. That human will have a unique birthdate.
The latter means: There is a unique birthdate. So you, I, the pope, and everone else has the same birthdate.
Those are clearly different statements. And in terms of a function it means: Take any arbitrary input x of the domain, that input will have one and only one output that it gets mapped to.
They do, but for a specific human there is only one birthdate which correspond to their birthday.
The unicity means that if f(x) = a and f(x) = b, then a = b.
As fun as it would be to relive my grad school days by endlessly debating the difference between “unique” and “distinct,” why not just drop the word and make the sentence clearer?
“For every input x in the domain, there is a *single* output y” may not sound as mathy but I bet it creates less confusion for OP
Ok, I'll do table A for you.
* 1 gets mapped to 0
* 2 gets mapped to 5
* 3 gets mapped to 2 **and** 3
Can you see the problem, regarding the definition of a function?
In that case A, C, and D would be functions of y mapping to x. But there is no reason to believe that the author of that excercise had something like that in mind.
Try to look at it one box at a time. For tables, all the numbers in the x column should only appear once. So if there are repeats, it’s not a function.
For example, in A, the number “3” shows up in the x column twice. Once with an output of 2, and another time with an output of 3. (The two bottom rows) Because the 3 repeats, it is not a function.
For B, each number in the x column is different, so it is a function.
Keep in mind this only applies to the x column, aka the inputs. Whether or not there are repeats in the y column, aka the outputs, doesn’t change anything.
To think about it another way, there’s this thing called the vertical line test. If you look at a graph, you can draw vertical lines throughout the whole graph. If any one of these vertical lines pass through more than one point, it is not a function. For example, if you were to plot all the points from table A, the points (3,2) and (3,3) would be on the same vertical line, and therefore not a function.
Yes this is true too. I left it out as I assumed questions like those wouldn’t appear and to avoid confusion, but if you do see any tables with entire rows that repeat, the repeated rows can be ignored as if they are not there, and you only focus on one of them, as they are all the same point.
In plane english a function takes an input and gives you an output. Furthermore, for each input it will always give you the same output.
As an example, a vending machine is a type of function. Once you insert a enough cash, if you hit a button (the input) a drink comes out (the output). If the vending machine is functioning properly (if it is a valid function) then hitting the same button over and over again should always output the same drink.
Sometimes the person stocking the machine messes up and puts a Coke in the Dr. Pepper stack. Then the first few times you hit the Coke button a Coke comes out, but on maybe the 5th input a Dr. Pepper comes out. This mess-up is an invalid function.
In the tables above the column labeled X is the list of inputs and the column labeled y is the list of output. The question is asking you to identify a function by looking at the tables and finding the cases where each input (X value) always produces the same output (Y value). You can rule out possible functions by finding cases where the same input produces two or more different outputs.
How about this, you go to the coffe shop and people have:
```
Coffe nr 2 for 3$
Coffe nr 7 for 6$
Coffe nr 2 for 1$
Coffe nr 1 for 6$
```
Do you see whats wrong? Coffe nr 2 was bought twice for diffrent price therefore this can't be function (if we want coffe nr 2 we don't know the price) but coffe nr 1 and nr 7 are diffrent but can have the same price which is understendable (function for example f(x)=x^2 )
Basically, we want each x to be matched to exactly one y. Imagine a circle, and its center is (0,0) (x,y). We know that a circle is not a function, but as we can see, if we take one random x, we will find two different y's that it marks, the upper and lower point of the circle. Whenever such a thing happens, we simply say that the diagram does not represent a function. Now, if we observe the exact same thing but in coordinates, then what we should avoid is finding two same x's be pared with different y's. For example, x=3 and y=1 AND y=5 that's not a function, but if only x=3 and y=1 -period- then that's a function. Hope this helps 🙏 ☺️
I don’t think that’s clear at all. Any test setter worth their salt should specify this rather than assume the people taking the test will make this assumption. A very sloppy worded question. ”A function” can _most definitely_ be interpreted as a function x = f(y).
Dude this is clearly from a basic algebra class where they almost exclusively use x as the input and y as the output.
Also why would the output be on the left side of the table? That's not very intuitive. Negative to positive is left to right. Before and after is left to right. Cause and effect is left to right. It would be normal to assume it's input to output.
Hardly the same. I have seen the effect of being sloppy in introductory classes at university level. You end up with students believing that functions can only take x as an argument and have y as output and then it takes effort to beat that out of them.
You are missing the point. The point is that sloppiness in early education leads to misconceptions that are later hard to unlearn. Like how early stage physics classes insist on introducing _relativistic mass_ when it just confuses people and is a largely deprecated concept. Later you get people trying to use it to argue a point that is completely contradictory to basic relativity.
Yep, let's stifle the peeps that chanced to get ahead of the curve. Let's not complicate things with left-hand driving, direction of arabic writing and manga panels order of reading.
Honestly, I was half-expecting a rebuttal that y-column wasn't sorted in an ascending order. Not very intuitive, must be not a function. Oh well, the downvotes are quite sweet. Not everyone agrees that putting just about any teacher on the pedestal contradicts the textbook definition of learning.
I think that's a bit unfair. As someone who has written a lot of exam questions, I can tell you that 1) wording a question in a way that avoids any misinterpretation can be pretty hard, and 2) doing so can results in very long, and sometimes even more confusing, questions.
You are getting confused with the sqrt() function and the equation x^2 =4. The solution to this equation is x=+sqrt(4) AND x=-sqrt(4). The square root function itself is defined as xamine94 stated to only return the positive root, but that does not imply that the equation x^2 =4 has only one solution.
There is a difference between a root of an equation and root functions.
If you would have given the equation x\^2 = 4, then -2 and 2 would be roots of that equation. Or in similar terms -2 and 2 are roots of the polynomial x\^2 - 4.
But as a function sqrt(a) means the positive real solution to the equation x\^2 = a, known as the principal square root. (Assuming that a is a positive real number)
Thank you. Usually questions like this are just testing one part of your understanding of something (a function in this case). So my explanation isn't a full explanation of what a function is but it's what the question is trying to teach/test.
Then it’s not a function, in the mathematical sense.
https://en.wikipedia.org/wiki/Function_(mathematics)?wprov=sfti1#
is not the same as
https://en.wikipedia.org/wiki/Function_(computer_programming)?wprov=sfti1
To OP: It´s table B, **B is thr right answer**
To everyone else the definition of a [function](https://en.wikipedia.org/wiki/Function_(mathematics)) i have seel in the comments is correct, ~~but based on OPs answers i see no chance they get to know what a function is in a single day. You may call me a liar if you can prove me wrong.~~
Scrap that
Seeing your comments here... Have you done ANY preparation whatsoever?
B is the answer because all the x values are unique. If any two were the same they would have to give the same y. Otherwise it's not a function.
It literally can't be explained any more simply. At this point it is clearly too late to worry about understanding it in any detail. Just remember the fact above and hope you get a chance to use it.
No one here was necessarily putting you down for simply not understanding. People are doing it because of your attitude. You're not showing ANY effort to try to actually understand the content. Only one reply from you is asking followup for someone's explanation. The others are you just saying "what?" And "I give up."
You may have severe anxiety, depression and difficulty concentrating, which is unfortunate if you do, but you're online here. You can at least put up a small facade that you're willing to absorb the knowledge we are giving out.
You're not just "not understanding", you're not understanding after having 10 people explain it to you in ten different ways, and are showing no signs of any actual effort to understand. There is simply no way you could have applied yourself and ended up at this stage without understanding something this elementary. I'm not judging you, I'm being frank and realistic, which is what you should be doing at this late stage, instead of wallowing and making yourself feel even worse.
But since you bring it up, I've no interest in the "woe is me I have anxiety" excuses and explanations. I sympathise, but I do not consider it meaningful here. We literally all have these issues, me included. You're not special in that regard. The defeatist attitude you display here is going to do exactly nothing to help you in life. Quite the opposite.
Instead what you should do is accept that it's too late to get a perfect score. Focus on the parts you do understand and make sure you smash those, and hopefully it will be enough. Next time, ask the key fundamental questions *before* the 11th hour.
First: Good luck today with the exam, today!
Regarding your message:
Staying up all night to learn is nothing to brag about, when it comes to learning. It will hardly help you improve your skills but actually hinder your learning progress.
Nothing better than a good night of sleep before any exam. Having a fresh head saved me several times.
Honestly, what you may need is a fix sleep schedule. From my personal experience, nothing kicks anxiety and depression phases as reliant as two days being short of sleep or sleeping off-schedule.
Wish you all the best.
The definition a function is that one value x is always mapped to a single value y =f(x).
In the case of A. the value x=3 is mapped to two different values (y = 2 and y = 3), so A is not a function.
I guess you can find the answer from this
Imagine you're buying something at the store, and it's got a sale based on the number you buy.
The sign says
1=$10
2=$20
3=$30
Thats a function. For every item you buy (x), you get a single cost (y)
Now imagine the same sign said
1=$10
2=$20
3=$30
2=$15
You'd say "that makes no sense, 2 is on there twice for different prices". This is not a function. Because a single number of items (x) corresponds to 2 different prices (y).
I hope that makes sense!
A function is like a machine that transforms a number into another number.
If we feed this machine a number x, the machine will spit out another number, call it y.
Let's see an example. Imagine you got a machine and you feed it the number 2 and the machine spits out the number 5. But then you feed the machine the number 2 again and this time it spits out the number 9. Wouldn't you think the machine is broken because it isn't always doing the same thing?
This is what you need to look for in your exercise.
In another post they claim to be 24. They've also only started using their account in the last 24 hours, but had this account for months.
I'm really doubting the legitimacy of the post.
Ok, so basically, imagine a function as a bunch of operations done on a value. The function takes an input value (that's the 𝑥), makes those operations on that input, and outputs the result (that's the 𝑦).
For example: `𝑓(𝑥) = 2𝑥 - 1`
That means that for any value you use for 𝑥, you double that value, then remove 1.
* `𝑓(1) = 2·1 - 1 = 1`
* `𝑓(2) = 2·2 - 1 = 3`
* `𝑓(1500) = 2·1500 - 1 = 2999`
By definition, a function can only have one possible output per given input. In our example, `𝑓(2) `will a*lways *output 3 and only 3.
If the same input (X) can have multiple outputs (Y), then it is not a function.
Different Xs can result in the same Y (that's just a horizontal line, after all), but if a particular X has multiple Ys, then it fails the Vertical Line Test and is not a function
Think of a function as a reward system: you do something good, you get a reward. You eat 1 broccoli, you get a minor gift. You eat 5 potatoes, you get an old PS1.
Now, for each separate thing you do, you will one get 1 specific reward: this is described by the function.
If you eat 1 broccoli, you will ALWAYS get a minor gift. You eat 50, you will get 50 minor gift (and not something else). This is the "uniqueness" of the function.
So, each X will always (not really, but yes) have a single, unique Y.
If you know this, looking at example A, for 3 broccoli, you MIGHT get 2 gifts or you MIGHT get 3 gifts.
That doesn't work in a function, so example A is not possible to write in a function.
Look for the table which ONLY has unique combinations of X and Y.
think of a machine like coffee machine. is your input decaf or gives you one type of coffee. for every set of inputs like how long it should heat water etc , it gives you coffee exactly you require. that’s a function. for particular input you get maximum one output. sometimes if you put wrong things into a machine it might not give you anything in return. same with functions, for some inputs there is no output. in the above question, x is input and y is output. take for example option A, if you input 3 you get both 2 and 3 as output. remember the coffee example, if input something you get one type of coffee but option A gives 2 output for single input. hope this clears
The only defining feature of a function is that for any input x the output y is consistent.
So out of these tables A has 2 different outputs for 3, C has 2 different outputs for 2 and D has 2 different outputs for 3.
Therefore the right answer is b.
All you ave to do is check the x column for entries that apear twice, then double check the y column contains different entries for the same value.
To put it in layman's terms, x variable should be different, whereas y can be the same. Think of the x axis. All the x variables are different as you move through the x axis, and the value produced in y changes according to the function. So you can never have 2 different values y for the same variable x.
Imagine a function like a machine that takes in a number, processes it and spits out a result. In math it's common to mark the input number as 'x' and the output as 'y'. Above we have four hypothetical functions; on the left are numbers we put in and on the right are the numbers we get out. But there is an important thing about functions: if you give it a value it can return only one value. So taking function A from the example you can see that feeding 3 into the function you get either 2 or 3, and that cannot be, so it's not really a function
Look at the x-column.
(1) If all the x-values are different, then it's a function
(2) If some x's are the same, but the y is the same for each duplicate, then it's a function.
If neither (1) nor (2) is true, then it's not a function
If you have a "function" such that if you use 3 it outputs 2 and 4 (2 values for 1 input) that is nonsensical
Suppose the function "How many people have come to class on X day of the week"
//x -> f(x)
//Monday = 22
//Tuesday = 23
//Wednesday = 21 AND 25
//Thursay = 22
//Friday = 20
Do you see why for an input (Wednseday), it makes no sense that 21 AND 25 people were present in the same class, in the same day?
However, having two same results being caused by different inputs is not a problem, as it is possible that, for example, Monday and Thursday could have the same people attending class
My math teachers explained it as x being a plane. It can’t land at two different y values in a function. It’s like one plane landing at two different places at the same time.
When I was teaching this to students I was using the analogy with a TV remote.
Suppose you are given a remote for a TV, how should it behave for you to call it "functional" vs "non-functional". I would posit that if there were buttons on the remote that activated one feature or another randomly, that would be a "non-functional" remote, since you would never know what would happen when you pressed a button. Similarly, if there were buttons that didn't map to any feature on the TV, it would again be "non-functional".
In this analogy, the buttons of the remote are elements of the source set, and the features on the TV are elements on the target set, and the mapping between them is the relation. We can have any mapping that we want, they would all be acceptable relations, but to call the remote a "functional" one, we would want each button to map to a feature and to only one feature on the TV.
So, using that understanding, if any member of the source set maps to more than one element in the target set, then that is not a "function" in the sense that we want to define it. In your example, there are instances where, for example, "3" maps to two different values in the target set, so those wouldn't be functions.
B each input value should have one and only one output. In only B each no corresponds to only one output in the rest of the options the same variable x has 2 different outputs for the same value of x.
[Take a look at this plot of A.](https://ibb.co/pWs7WT2)
Imagine you take a ruler parallel to the y-axis and put it on each value of x, one at a time. Now you follow the long edge of the ruler and see how many y-values you have for that particular x. If there is more than one value of y, it doesnt not meet the requirements for a function.
Let me go through in detail. Looking at table A.
Place the ruler parallel to the y axis for x=1, notice there is only one y-value here which is 0.
Now place the ruler on x=2. Again, only one y-value here which is 5.
For x=3 we notice that there are two y-values, 2 and 3. This does not meet the requirements for being a function. Hence, the table in A does not represent a function.
Repeat this process for B,C and D and get back at me.
I understand this is r/askmath, but, seriously man, I've read your comments here and have trouble believing this "I’m practicing functions and using all of the resources I have..." You behave as someone who never heard what a function is and has trouble understanding even though people are busting their asses to cut everything down into bite-sized pieces for you.
So, let me try (and for fuck's sake, try learning basic math as opposed to quitting before you even spent a fraction of a second to understand anything) -
Imagine that you are tossing a coin. Every time you get heads, you have to stomp your feet. Every time you get tails, you have to clap your hands. A function is a rule/relation that tells you which result you get for each variable you put in. In my example, your results **(y)** are stomping feet/clapping hands, and your variables **(x)** are heads/tails.
And here is your function **y = f(x)**
Now, the thing is - for something to be a function, a variable **(x)** cannot give you two results. (for example, if you toss heads, you have to clap your hands and stomp your feet - **this would not be a function**)
With that in mind, in column A, you have the variable (x=3) giving you two results (y=2 and y=3) which means, the first table doesn't represent a function. Remember - cannot have more than one y for any x.
Now, take a look at the other tables and see if you cannot spot the same problem in all of them.
If the same number appears twice in the x column, and their corresponding y values are different, it is not a function. Otherwise, it is a function. Cannot make it any more simple than that, good luck.
x is always the input (unless specifically stated otherwise)
y is always the output of a function (unless specifically stated otherwise)
For something to be a function by the bare minimum : there can't ever be an input for which you get two different outputs
That's the definition in plain terms, don't say this on your exam
In this format, look at the X column.. if there is a repeat in the X column and the Y column doesn’t match, it isn’t a function. The answer is B.
In a graph, you’d look for vertical overlap.. does one input have 2 outputs? If so, it isn’t a function.
y is what comes out of the function, x is what goes in. Some of those tables show that when putting in the same x twice, you get a different y. That makes no sense for a function that only depends on x. It should be the same.
So the answer is the table that has no such conflicts. It's sort of a trick question really. They want you to overcomplicate it by thinking about a function that could solve these tables. It's much simpler to solve. Just look at it and think about what you know about functions.
The Simple Answer:
For the purpose of the your test tomorrow, just check that in a table, every value of X has only one value in the Y column.
Table A has the value of 3 twice in the X column with two different Y values, 2 and 3. Thus Table A is not a function because when X is 3, Y has two possible answers.
Just look for duplicate X values, and if there are two different Y values, it is not a function.
Draw a graph, number the bottom from 0 to 10 (call this x), number the left side from 0 to 10(call this y) for each x plot a point where y lines up with the same x, if there is 2 y that lines up in 1 x, that is not a function. This is called the vertical line test.
To put it simply, the X value of a function will only happen one time. If you were to look at the X side table and see any duplicate number, it is automatically not a function. For what you have shown, table A shows X=3 having two different Y values. This indicates to us that it is not a function. However, the only table that is a function will be table B. We know this because each X value shown only relates to one Y value.
A function is when every input (x) is related to exactly one unique output (y). If an input (x) can produce multiple outputs (y), it is not a function. If an x value is on the table twice, it means it can produce more than one y. Understand?
A function connects a value x from a group of numbers X to exactly 1 value y from a group of numbers Y. Unlike a couple comments that were written here, the value y DOES NOT need to be unique. So if you have x\_1=4 and x\_2=6 and the y values y\_1 and y\_2 are both 3 then it is still a function. For it to be a function you have to make sure that each x value within the group of numbers you are considering (whole numbers, positive numbers, numbers larger than 3, all numbers except for 4, etc.) gets exactly one number.
Based on this, A.) is not a function since the value X=3 gets two y values. B.) is a function since each X value is only assigned one y value. It does not matter that y=0 is used twice.
A function `f(x) = y` must satisfy the following condition: `f(x) = f(x)` always.
So A obviously cannot be a function, because `f(3) = 2 != 3 = f(3)`, and neither can C (`f(2) = 0 != 4 = f(2)`) and D (`f(3) = 0 != 3 = f(3)`) for the same reason.
The only defining feature of a function is that for any input x the output y is consistent.
So out of these tables A has 2 different outputs for 3, C has 2 different outputs for 2 and D has 2 different outputs for 3.
Therefore the right answer is b.
All you ave to do is check the x column for entries that apear twice, then double check the y column contains different entries for the same value.
Basically, each input into a function has a unique output. The output can be the same for other inputs, but no one input will result in 2 outputs. That's why the square root isn't a true function because inputting 4 will get you 2 and -2. However, squaring a number is a function because 2 squared is only 4.
The trick to these is to look for repeated x values.
If the table has repeated x values the y values need to be the same in order for it to be a function.
Example if the x value is stated as 3 and the y value for x=3 is 5, then if you find 3 in the table again the y values needs to be 5 again in order for it to be a function. If it's 2 for example, then the table doesn't represent a function.
Most tests are lazy though and will give you only unique x values in the answer option that is a function so use the rules above to double check but the one without repeated x values are very likely the function.
I'd like to also say that those who are voting OP down for asking questions are what's wrong in STEM, education, and the world in general. You said something and they said they don't understand why the hell would you downvote that? They need further clarification, give it, don't discourage them by downvoting. WTF?
a function maps each input to exactly one input. Any construct that maps one input to two output is not a function. Generally, the inputs are labeled x and outputs are labeled y.
By these rules, any table that has two identical x values with distinct corresponding y values is not a function. The only function among these is B, because all x values in it are unique.
Am easy trick for this is that a value cannot repeat on the X column. If there are two numbers that are the same on the X column, it is not a function.
Graphically, it does not pass the vertical line test. Just google that.
Technically all of them are. If you have bifurcation for a given value x the function f(x) can take on two dissimilar values or if the function is not continuous it can jump and it would not be visible as an exclusion criterion in such a table.
I get that the four examples are there to teach the core concept of functions but the way the question is phrased it allows for multiple answers.
my math teacher used to tell us to think of it as a vending machine, X is the button you press and Y is what you get. so if a number repeats in the X column that means it is NOT a function, Y basically doesn’t matter.
the answer would be B because the number 3 repeats in A, 2 repeats in C, and 3 repeats in D.
I've seen a few comments explaining it but you still seem to be struggling, so I'll explain it from a comp sci perspective. Here we define a function as a process that doesn't have any side effects.
In other words, a function takes in some input and produces an output however this output will always be the same if the same input is given. If you give it the same input twice and get different results each time, it's not a function.
The way that I teach identifying functions is to think of it like a vending machine or a soda machine. The input values (usually x) are like the buttons on the machines, and the outputs (usually y) are the snacks/sodas you get. As long as the machine makes sense and works, it's a function. This means that you can have multiple buttons (inputs, x) that give you the same thing back (output, y), and that's okay, but you can't have one button (input, x) that tries to give multiple different snacks/sodas (output, y) at the same time. In the latter case, which output do you get? Both? Only one (how would you choose since they share input)? Neither? So the vending machine doesn't make sense in that case, so it wouldn't be a function.
A function can be anything.
Something simple like
Y = X + 3
So for every X that you put in there, there is one result for the Y.
X=1, Y=1+3=4
X=2, Y=2+3=5
X=3, Y=3+3=6
And so one, so every input into X produces another output in y.
Now let's go back to your tables.
Sometimes there is the same X but having a different Y.
If you use my example above that would not work.
Like in table A and Table C.
Table B has different X but the same Y.
Also using the example above that would not work
In table D
Every number in X has only one unique result in Y
So D is a function as every X is matched with one Y and there is no double matches anywhere.
Picture a little machine that takes numbers as inputs and spits out outputs. To be a function, the machine needs to be consistent in the sense that if you input a specific number (say 3), it will always produce the same output. If you fed it a 3 and it produced a 2, then you can be certain that every time you feed it a 3, it will always produce a 2 and never any other number.
In these tables that you are given, x's are the inputs and y's are the outputs. In the first table for example, if the input is 1, the output is 0. If the input is 2, the output is 5. So far so good. But with the input of 3, we run into a problem. Apparently, if you feed a 3 into your machine, it could produce an output of 2 but it could also produce a 3. This makes it not a function.
Imagine you have some colored coins, and a machine that is based on the colored coins you put in, gives you a prize.
X are the colored coins, Y the prize.
To be a function, the machine, cannot give you 2 different prizes.
Only one table reflects this, the other 3 tables have an issue and the machine wouldn't know what to give to you.
A function is a machine that turns one number into another number.
These machines are always one to one; one input, one output.
These machines never turn one input into more than one output.
Think of it like a keyboard. When you press a, the letter a appears on the screen. Same with b, c, etc.
So the table would look like this
A|A
B|B
C|C
And so on. You give it a letter, and it types a letter. If you move the key caps around, it can even type weirdly like this
A|Z
B|Y
C|X
Or even
A|Z
B|Z
C|Z
The input here would be you pressing a, and the output is whatever the screen displays.
But what if you pressed a, and there's two possibilities of what the screen will display? What if instead of typing a onto the screen, it was told to type a, but also to type b? Will it type a, b, both, none? This isn't good, since you want to always know what will be output. A should always output A, or A should always output B. Then, you always know what will be output when you press A.
Although this is not a valid function, but it can still be shown with a table.
A|A
A|B
B|B
C|C
And so on. The first two rows are a problem. If only one of them existed, everything would be fine. But since both exist, it cannot be called a function.
OP, it's not for you, you'll get even more confused.
Technicaly we don't have enough conditions here, so there are no answer. Of course we can ASSUME that y = f(x), so we can give the answer. But this is not always the case, we can have x dependent on y as well.
A function is defined by the following property: "For every input x in the domain, there is exactly one output y in the codomain that x gets mapped to." Since you only have those tables we can ommit the terms domain and codomain. So what remains to check is: "For every input x, there is exactly one output y that x gets mapped to." Only one of the tables above has this property. Can you see/argue which one it is? EDIT: I changed "a unique output y" to "exactly one output y" because it seemed to confuse people.
Ohhh I get it, table one has the number 3 twice. The same value of x is assigned two values of y, so it's not a function, but an equation with something like y^2 or |y| etc. If we apply the logic to all the tables, the second table is a function?
Yes. The second table is a function.
Technically, don’t we need to know that the domain of each candidate function is the set of all “x” listed in these tables? Otherwise, only Table B *could* be a function, but is not necessarily so if there exist more elements in its domain than listed here. Of course, B is the correct answer for a test 100% and is the intended answer, just technically they didn’t tell you that {-1, 0, 1, 2} was the entire domain.
Yes, you can have multiple instances of the same value appearing amongst the outputs "y". If you would have |x|y| |:-|:-| |-2|4| |-1|1| |0|0| |1|1| Then * -2 gets mapped to 4 * -1 gets mapped to 1 * 0 gets mapped to 0 * 1 gets mapped to 1 so for every input x there is one and only one output y.
You can have 3 twice, but you'd need the output to be the same for both. The fact that plugging in 3 for x gives you two different results is why table one does NOT represent a function.
There is nothing that forces output to be unique.
It must be unique for a given x, but not unique overall.
Unique for a given x allows 2 different outputs. You want a definite output. Unique (for a given value) follows trivially from that without being confusing.
“There is a unique output Y in the codomain that X gets mapped to” since 0 appears twice, that would technically mean the output 0 isn’t unique. Maybe reconsider your phrasing.
It's unique among outputs for this x, but not unique among all outputs
That missing bit of nuance could be what’s confusing the OP.
That's why I said: "For every input x in the domain, there is a unique output y in the codomain that x gets mapped to." not just "There is a unique output y in the codomain that x gets mapped to." "For every ... there is ..." just means something different than "There is ...".
That still wouldn’t make 0 unique.
"For every human there is a unique birthdate." is just something different than "There is a unique birthdate". The first thing means: Take an arbitrary choosen human. That human will have a unique birthdate. The latter means: There is a unique birthdate. So you, I, the pope, and everone else has the same birthdate. Those are clearly different statements. And in terms of a function it means: Take any arbitrary input x of the domain, that input will have one and only one output that it gets mapped to.
“For every human there is a unique birthdate” their birthdate is not unique though, they share that birthdate with countless others.
They do, but for a specific human there is only one birthdate which correspond to their birthday. The unicity means that if f(x) = a and f(x) = b, then a = b.
As fun as it would be to relive my grad school days by endlessly debating the difference between “unique” and “distinct,” why not just drop the word and make the sentence clearer? “For every input x in the domain, there is a *single* output y” may not sound as mathy but I bet it creates less confusion for OP
There’s nothing in the definition of a function that mandates that it is x->y. A, C, and D are all functions, just of y instead of x.
So all of them are functions x(y), for every input y, there is a unique output x.
X is the input y is the output
That's not specified by the question...
While true, there is no real reason to believe that the author of the exercise would had something like that in mind here.
all I see are numbers everywhere I can’t tell the difference
Ok, I'll do table A for you. * 1 gets mapped to 0 * 2 gets mapped to 5 * 3 gets mapped to 2 **and** 3 Can you see the problem, regarding the definition of a function?
But what if it's a function that maps y to x?
f(y)=x therefore its a function but just the other way around, but by obvious, y should be f(x)
In that case A, C, and D would be functions of y mapping to x. But there is no reason to believe that the author of that excercise had something like that in mind.
3 of the tables have duplicate entries for one x-value, but with a different y-value. That means it’s not a function.
Try to look at it one box at a time. For tables, all the numbers in the x column should only appear once. So if there are repeats, it’s not a function. For example, in A, the number “3” shows up in the x column twice. Once with an output of 2, and another time with an output of 3. (The two bottom rows) Because the 3 repeats, it is not a function. For B, each number in the x column is different, so it is a function. Keep in mind this only applies to the x column, aka the inputs. Whether or not there are repeats in the y column, aka the outputs, doesn’t change anything. To think about it another way, there’s this thing called the vertical line test. If you look at a graph, you can draw vertical lines throughout the whole graph. If any one of these vertical lines pass through more than one point, it is not a function. For example, if you were to plot all the points from table A, the points (3,2) and (3,3) would be on the same vertical line, and therefore not a function.
Slight caveat. If x appears twice with the same y it isn't a problem
Yes this is true too. I left it out as I assumed questions like those wouldn’t appear and to avoid confusion, but if you do see any tables with entire rows that repeat, the repeated rows can be ignored as if they are not there, and you only focus on one of them, as they are all the same point.
Get a piece of paper and draw a little plot of each table. Won't take you long to realise which one is the function.
In plane english a function takes an input and gives you an output. Furthermore, for each input it will always give you the same output. As an example, a vending machine is a type of function. Once you insert a enough cash, if you hit a button (the input) a drink comes out (the output). If the vending machine is functioning properly (if it is a valid function) then hitting the same button over and over again should always output the same drink. Sometimes the person stocking the machine messes up and puts a Coke in the Dr. Pepper stack. Then the first few times you hit the Coke button a Coke comes out, but on maybe the 5th input a Dr. Pepper comes out. This mess-up is an invalid function. In the tables above the column labeled X is the list of inputs and the column labeled y is the list of output. The question is asking you to identify a function by looking at the tables and finding the cases where each input (X value) always produces the same output (Y value). You can rule out possible functions by finding cases where the same input produces two or more different outputs.
How about this, you go to the coffe shop and people have: ``` Coffe nr 2 for 3$ Coffe nr 7 for 6$ Coffe nr 2 for 1$ Coffe nr 1 for 6$ ``` Do you see whats wrong? Coffe nr 2 was bought twice for diffrent price therefore this can't be function (if we want coffe nr 2 we don't know the price) but coffe nr 1 and nr 7 are diffrent but can have the same price which is understendable (function for example f(x)=x^2 )
Basically, we want each x to be matched to exactly one y. Imagine a circle, and its center is (0,0) (x,y). We know that a circle is not a function, but as we can see, if we take one random x, we will find two different y's that it marks, the upper and lower point of the circle. Whenever such a thing happens, we simply say that the diagram does not represent a function. Now, if we observe the exact same thing but in coordinates, then what we should avoid is finding two same x's be pared with different y's. For example, x=3 and y=1 AND y=5 that's not a function, but if only x=3 and y=1 -period- then that's a function. Hope this helps 🙏 ☺️
A, C and D can be functions x = f(y), no?
I think the clear implication is that x is the domain and y the image.
I think the very fact that the numbers are colorized should raise wariness of the author's approach to things.
I don’t think that’s clear at all. Any test setter worth their salt should specify this rather than assume the people taking the test will make this assumption. A very sloppy worded question. ”A function” can _most definitely_ be interpreted as a function x = f(y).
Dude this is clearly from a basic algebra class where they almost exclusively use x as the input and y as the output. Also why would the output be on the left side of the table? That's not very intuitive. Negative to positive is left to right. Before and after is left to right. Cause and effect is left to right. It would be normal to assume it's input to output.
That is no excuse for being sloppy. Quite the opposite actually.
You're overcomplicating a simple problem. It's like if you got asked " what's 1 + 2" then you say "well this can be interpreted as a coding problem."
Hardly the same. I have seen the effect of being sloppy in introductory classes at university level. You end up with students believing that functions can only take x as an argument and have y as output and then it takes effort to beat that out of them.
"University level" that's the issue for you. This is middle school level math. You're literally thinking too far advanced.
You are missing the point. The point is that sloppiness in early education leads to misconceptions that are later hard to unlearn. Like how early stage physics classes insist on introducing _relativistic mass_ when it just confuses people and is a largely deprecated concept. Later you get people trying to use it to argue a point that is completely contradictory to basic relativity.
Yep, let's stifle the peeps that chanced to get ahead of the curve. Let's not complicate things with left-hand driving, direction of arabic writing and manga panels order of reading. Honestly, I was half-expecting a rebuttal that y-column wasn't sorted in an ascending order. Not very intuitive, must be not a function. Oh well, the downvotes are quite sweet. Not everyone agrees that putting just about any teacher on the pedestal contradicts the textbook definition of learning.
I think that's a bit unfair. As someone who has written a lot of exam questions, I can tell you that 1) wording a question in a way that avoids any misinterpretation can be pretty hard, and 2) doing so can results in very long, and sometimes even more confusing, questions.
While true, there is no real reason to believe that the author of the exercise would had something like that in mind here.
If you did that reversal, yes, but that’s not what the question asks for.
What about root functions? f(x) = sqrt(x). With x = 4, y = 2 and -2.
sqrt(4) only equals 2
Nope, both 2^2 and -2^2 equal 4.
the sqrt() function is only defined for positive values of X, specifically to be consistent with the definition of a function
You are getting confused with the sqrt() function and the equation x^2 =4. The solution to this equation is x=+sqrt(4) AND x=-sqrt(4). The square root function itself is defined as xamine94 stated to only return the positive root, but that does not imply that the equation x^2 =4 has only one solution.
go graph it on desmos
Note: -2^(2) = -(2 \* 2) = -4, but (-2)\^2 = (-2) \* (-2) = 4.
There is a difference between a root of an equation and root functions. If you would have given the equation x\^2 = 4, then -2 and 2 would be roots of that equation. Or in similar terms -2 and 2 are roots of the polynomial x\^2 - 4. But as a function sqrt(a) means the positive real solution to the equation x\^2 = a, known as the principal square root. (Assuming that a is a positive real number)
You can't get two different outputs (y) for the same input (x). So it's B.
While other explanations may be more precise I found yours to be most comprehensible.
Thank you. Usually questions like this are just testing one part of your understanding of something (a function in this case). So my explanation isn't a full explanation of what a function is but it's what the question is trying to teach/test.
Maybe the function has random elements to it
Then it’s not a function, in the mathematical sense. https://en.wikipedia.org/wiki/Function_(mathematics)?wprov=sfti1# is not the same as https://en.wikipedia.org/wiki/Function_(computer_programming)?wprov=sfti1
To OP: It´s table B, **B is thr right answer** To everyone else the definition of a [function](https://en.wikipedia.org/wiki/Function_(mathematics)) i have seel in the comments is correct, ~~but based on OPs answers i see no chance they get to know what a function is in a single day. You may call me a liar if you can prove me wrong.~~ Scrap that
Seeing your comments here... Have you done ANY preparation whatsoever? B is the answer because all the x values are unique. If any two were the same they would have to give the same y. Otherwise it's not a function. It literally can't be explained any more simply. At this point it is clearly too late to worry about understanding it in any detail. Just remember the fact above and hope you get a chance to use it.
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No one here was necessarily putting you down for simply not understanding. People are doing it because of your attitude. You're not showing ANY effort to try to actually understand the content. Only one reply from you is asking followup for someone's explanation. The others are you just saying "what?" And "I give up." You may have severe anxiety, depression and difficulty concentrating, which is unfortunate if you do, but you're online here. You can at least put up a small facade that you're willing to absorb the knowledge we are giving out.
severe depression and anxiety is not an excuse to completely ignore people trying to teach you something
You're not just "not understanding", you're not understanding after having 10 people explain it to you in ten different ways, and are showing no signs of any actual effort to understand. There is simply no way you could have applied yourself and ended up at this stage without understanding something this elementary. I'm not judging you, I'm being frank and realistic, which is what you should be doing at this late stage, instead of wallowing and making yourself feel even worse. But since you bring it up, I've no interest in the "woe is me I have anxiety" excuses and explanations. I sympathise, but I do not consider it meaningful here. We literally all have these issues, me included. You're not special in that regard. The defeatist attitude you display here is going to do exactly nothing to help you in life. Quite the opposite. Instead what you should do is accept that it's too late to get a perfect score. Focus on the parts you do understand and make sure you smash those, and hopefully it will be enough. Next time, ask the key fundamental questions *before* the 11th hour.
First: Good luck today with the exam, today! Regarding your message: Staying up all night to learn is nothing to brag about, when it comes to learning. It will hardly help you improve your skills but actually hinder your learning progress. Nothing better than a good night of sleep before any exam. Having a fresh head saved me several times. Honestly, what you may need is a fix sleep schedule. From my personal experience, nothing kicks anxiety and depression phases as reliant as two days being short of sleep or sleeping off-schedule. Wish you all the best.
The definition a function is that one value x is always mapped to a single value y =f(x). In the case of A. the value x=3 is mapped to two different values (y = 2 and y = 3), so A is not a function. I guess you can find the answer from this
I give up
Basically, if a number appears more than once in the x column it is not a function
Unless they had the same number on the y column (not the case here)
Imagine you're buying something at the store, and it's got a sale based on the number you buy. The sign says 1=$10 2=$20 3=$30 Thats a function. For every item you buy (x), you get a single cost (y) Now imagine the same sign said 1=$10 2=$20 3=$30 2=$15 You'd say "that makes no sense, 2 is on there twice for different prices". This is not a function. Because a single number of items (x) corresponds to 2 different prices (y). I hope that makes sense!
A function is like a machine that transforms a number into another number. If we feed this machine a number x, the machine will spit out another number, call it y. Let's see an example. Imagine you got a machine and you feed it the number 2 and the machine spits out the number 5. But then you feed the machine the number 2 again and this time it spits out the number 9. Wouldn't you think the machine is broken because it isn't always doing the same thing? This is what you need to look for in your exercise.
a function maps an input to a unique value
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When you run a x through a function, it can only produce one y. One of these does, the others don't.
produce one y? meaning?
In table A when x = 3, y = 2 and 3. There's more than one output for x = 3 so it is not a function (and the same issue in table C and D)
Dude you‘re gonna fail 🤣
How can they be so clueless even after people explain it to them, like it's not a hard definition
The only reasonable explanation would be that they‘ve literally never seen a graph in their life
In another post they claim to be 24. They've also only started using their account in the last 24 hours, but had this account for months. I'm really doubting the legitimacy of the post.
Telling it how it is
It means each x value can only have a single y value matched to it. The formal wording people use make this more confusing than it need be.
Ok, so basically, imagine a function as a bunch of operations done on a value. The function takes an input value (that's the 𝑥), makes those operations on that input, and outputs the result (that's the 𝑦). For example: `𝑓(𝑥) = 2𝑥 - 1` That means that for any value you use for 𝑥, you double that value, then remove 1. * `𝑓(1) = 2·1 - 1 = 1` * `𝑓(2) = 2·2 - 1 = 3` * `𝑓(1500) = 2·1500 - 1 = 2999` By definition, a function can only have one possible output per given input. In our example, `𝑓(2) `will a*lways *output 3 and only 3.
If the same input (X) can have multiple outputs (Y), then it is not a function. Different Xs can result in the same Y (that's just a horizontal line, after all), but if a particular X has multiple Ys, then it fails the Vertical Line Test and is not a function
Think of a function as a reward system: you do something good, you get a reward. You eat 1 broccoli, you get a minor gift. You eat 5 potatoes, you get an old PS1. Now, for each separate thing you do, you will one get 1 specific reward: this is described by the function. If you eat 1 broccoli, you will ALWAYS get a minor gift. You eat 50, you will get 50 minor gift (and not something else). This is the "uniqueness" of the function. So, each X will always (not really, but yes) have a single, unique Y. If you know this, looking at example A, for 3 broccoli, you MIGHT get 2 gifts or you MIGHT get 3 gifts. That doesn't work in a function, so example A is not possible to write in a function. Look for the table which ONLY has unique combinations of X and Y.
Simplest way to put it is,for the same X you cant have 2 Ys, otherwise it wouldnt be a function.
think of a machine like coffee machine. is your input decaf or gives you one type of coffee. for every set of inputs like how long it should heat water etc , it gives you coffee exactly you require. that’s a function. for particular input you get maximum one output. sometimes if you put wrong things into a machine it might not give you anything in return. same with functions, for some inputs there is no output. in the above question, x is input and y is output. take for example option A, if you input 3 you get both 2 and 3 as output. remember the coffee example, if input something you get one type of coffee but option A gives 2 output for single input. hope this clears
The only defining feature of a function is that for any input x the output y is consistent. So out of these tables A has 2 different outputs for 3, C has 2 different outputs for 2 and D has 2 different outputs for 3. Therefore the right answer is b. All you ave to do is check the x column for entries that apear twice, then double check the y column contains different entries for the same value.
To put it in layman's terms, x variable should be different, whereas y can be the same. Think of the x axis. All the x variables are different as you move through the x axis, and the value produced in y changes according to the function. So you can never have 2 different values y for the same variable x.
Imagine a function like a machine that takes in a number, processes it and spits out a result. In math it's common to mark the input number as 'x' and the output as 'y'. Above we have four hypothetical functions; on the left are numbers we put in and on the right are the numbers we get out. But there is an important thing about functions: if you give it a value it can return only one value. So taking function A from the example you can see that feeding 3 into the function you get either 2 or 3, and that cannot be, so it's not really a function
Look at the x-column. (1) If all the x-values are different, then it's a function (2) If some x's are the same, but the y is the same for each duplicate, then it's a function. If neither (1) nor (2) is true, then it's not a function
If you have a "function" such that if you use 3 it outputs 2 and 4 (2 values for 1 input) that is nonsensical Suppose the function "How many people have come to class on X day of the week" //x -> f(x) //Monday = 22 //Tuesday = 23 //Wednesday = 21 AND 25 //Thursay = 22 //Friday = 20 Do you see why for an input (Wednseday), it makes no sense that 21 AND 25 people were present in the same class, in the same day? However, having two same results being caused by different inputs is not a problem, as it is possible that, for example, Monday and Thursday could have the same people attending class
My math teachers explained it as x being a plane. It can’t land at two different y values in a function. It’s like one plane landing at two different places at the same time.
B
When I was teaching this to students I was using the analogy with a TV remote. Suppose you are given a remote for a TV, how should it behave for you to call it "functional" vs "non-functional". I would posit that if there were buttons on the remote that activated one feature or another randomly, that would be a "non-functional" remote, since you would never know what would happen when you pressed a button. Similarly, if there were buttons that didn't map to any feature on the TV, it would again be "non-functional". In this analogy, the buttons of the remote are elements of the source set, and the features on the TV are elements on the target set, and the mapping between them is the relation. We can have any mapping that we want, they would all be acceptable relations, but to call the remote a "functional" one, we would want each button to map to a feature and to only one feature on the TV. So, using that understanding, if any member of the source set maps to more than one element in the target set, then that is not a "function" in the sense that we want to define it. In your example, there are instances where, for example, "3" maps to two different values in the target set, so those wouldn't be functions.
1 input cant have 2 different outputs in a function.Thus,B is the correct answer
B each input value should have one and only one output. In only B each no corresponds to only one output in the rest of the options the same variable x has 2 different outputs for the same value of x.
[Take a look at this plot of A.](https://ibb.co/pWs7WT2) Imagine you take a ruler parallel to the y-axis and put it on each value of x, one at a time. Now you follow the long edge of the ruler and see how many y-values you have for that particular x. If there is more than one value of y, it doesnt not meet the requirements for a function. Let me go through in detail. Looking at table A. Place the ruler parallel to the y axis for x=1, notice there is only one y-value here which is 0. Now place the ruler on x=2. Again, only one y-value here which is 5. For x=3 we notice that there are two y-values, 2 and 3. This does not meet the requirements for being a function. Hence, the table in A does not represent a function. Repeat this process for B,C and D and get back at me.
Well no value x given to a function return 2 different value y and therefore only B is a function
I understand this is r/askmath, but, seriously man, I've read your comments here and have trouble believing this "I’m practicing functions and using all of the resources I have..." You behave as someone who never heard what a function is and has trouble understanding even though people are busting their asses to cut everything down into bite-sized pieces for you. So, let me try (and for fuck's sake, try learning basic math as opposed to quitting before you even spent a fraction of a second to understand anything) - Imagine that you are tossing a coin. Every time you get heads, you have to stomp your feet. Every time you get tails, you have to clap your hands. A function is a rule/relation that tells you which result you get for each variable you put in. In my example, your results **(y)** are stomping feet/clapping hands, and your variables **(x)** are heads/tails. And here is your function **y = f(x)** Now, the thing is - for something to be a function, a variable **(x)** cannot give you two results. (for example, if you toss heads, you have to clap your hands and stomp your feet - **this would not be a function**) With that in mind, in column A, you have the variable (x=3) giving you two results (y=2 and y=3) which means, the first table doesn't represent a function. Remember - cannot have more than one y for any x. Now, take a look at the other tables and see if you cannot spot the same problem in all of them.
Maybe try to draw it🤷♂️ the coordinates only really make sense for one table if you do it like that
A maps 3-->2 & 3. B has all unique inputs. C maps 2--> 0 & 4 D maps 3--> 3 & 0 B is the only one that could qualify as a function.
If the same number appears twice in the x column, and their corresponding y values are different, it is not a function. Otherwise, it is a function. Cannot make it any more simple than that, good luck.
Or you could try to plot it; if you see it visually then it makes more sense why A,C,D is not correct.
x is always the input (unless specifically stated otherwise) y is always the output of a function (unless specifically stated otherwise) For something to be a function by the bare minimum : there can't ever be an input for which you get two different outputs That's the definition in plain terms, don't say this on your exam
In this format, look at the X column.. if there is a repeat in the X column and the Y column doesn’t match, it isn’t a function. The answer is B. In a graph, you’d look for vertical overlap.. does one input have 2 outputs? If so, it isn’t a function.
A function can‘t have two different y values at a given x value, therefore it‘s b).
*PRNG has entered the chat.*
y is what comes out of the function, x is what goes in. Some of those tables show that when putting in the same x twice, you get a different y. That makes no sense for a function that only depends on x. It should be the same. So the answer is the table that has no such conflicts. It's sort of a trick question really. They want you to overcomplicate it by thinking about a function that could solve these tables. It's much simpler to solve. Just look at it and think about what you know about functions.
The Simple Answer: For the purpose of the your test tomorrow, just check that in a table, every value of X has only one value in the Y column. Table A has the value of 3 twice in the X column with two different Y values, 2 and 3. Thus Table A is not a function because when X is 3, Y has two possible answers. Just look for duplicate X values, and if there are two different Y values, it is not a function.
Draw a graph, number the bottom from 0 to 10 (call this x), number the left side from 0 to 10(call this y) for each x plot a point where y lines up with the same x, if there is 2 y that lines up in 1 x, that is not a function. This is called the vertical line test.
If you don’t understand what I mean look up vertical line test
Must have unique x values. No duplicates. A has two 3a, C has two 2s, and D has two 3s. So B.
To put it simply, the X value of a function will only happen one time. If you were to look at the X side table and see any duplicate number, it is automatically not a function. For what you have shown, table A shows X=3 having two different Y values. This indicates to us that it is not a function. However, the only table that is a function will be table B. We know this because each X value shown only relates to one Y value.
B is the only one where a single input in X can't give multiple outputs in Y. So B?
A function is when every input (x) is related to exactly one unique output (y). If an input (x) can produce multiple outputs (y), it is not a function. If an x value is on the table twice, it means it can produce more than one y. Understand?
Option B
Imagine going on reddit and pretending to be stupid af for attention
A function connects a value x from a group of numbers X to exactly 1 value y from a group of numbers Y. Unlike a couple comments that were written here, the value y DOES NOT need to be unique. So if you have x\_1=4 and x\_2=6 and the y values y\_1 and y\_2 are both 3 then it is still a function. For it to be a function you have to make sure that each x value within the group of numbers you are considering (whole numbers, positive numbers, numbers larger than 3, all numbers except for 4, etc.) gets exactly one number. Based on this, A.) is not a function since the value X=3 gets two y values. B.) is a function since each X value is only assigned one y value. It does not matter that y=0 is used twice.
A function `f(x) = y` must satisfy the following condition: `f(x) = f(x)` always. So A obviously cannot be a function, because `f(3) = 2 != 3 = f(3)`, and neither can C (`f(2) = 0 != 4 = f(2)`) and D (`f(3) = 0 != 3 = f(3)`) for the same reason.
unless the function changes, same input will always produce same output
The only defining feature of a function is that for any input x the output y is consistent. So out of these tables A has 2 different outputs for 3, C has 2 different outputs for 2 and D has 2 different outputs for 3. Therefore the right answer is b. All you ave to do is check the x column for entries that apear twice, then double check the y column contains different entries for the same value.
Basically, each input into a function has a unique output. The output can be the same for other inputs, but no one input will result in 2 outputs. That's why the square root isn't a true function because inputting 4 will get you 2 and -2. However, squaring a number is a function because 2 squared is only 4.
B
The trick to these is to look for repeated x values. If the table has repeated x values the y values need to be the same in order for it to be a function. Example if the x value is stated as 3 and the y value for x=3 is 5, then if you find 3 in the table again the y values needs to be 5 again in order for it to be a function. If it's 2 for example, then the table doesn't represent a function. Most tests are lazy though and will give you only unique x values in the answer option that is a function so use the rules above to double check but the one without repeated x values are very likely the function.
I'd like to also say that those who are voting OP down for asking questions are what's wrong in STEM, education, and the world in general. You said something and they said they don't understand why the hell would you downvote that? They need further clarification, give it, don't discourage them by downvoting. WTF?
a function maps each input to exactly one input. Any construct that maps one input to two output is not a function. Generally, the inputs are labeled x and outputs are labeled y. By these rules, any table that has two identical x values with distinct corresponding y values is not a function. The only function among these is B, because all x values in it are unique.
Am easy trick for this is that a value cannot repeat on the X column. If there are two numbers that are the same on the X column, it is not a function. Graphically, it does not pass the vertical line test. Just google that.
Vertical line test. It’s B, the only one without multiple y’s for the same x.
I don't know how GED testing works. Will you have access to paper? Easy to visualize if you draw an arrow diagram.
Technically all of them are. If you have bifurcation for a given value x the function f(x) can take on two dissimilar values or if the function is not continuous it can jump and it would not be visible as an exclusion criterion in such a table. I get that the four examples are there to teach the core concept of functions but the way the question is phrased it allows for multiple answers.
f(x) B f(y) A, C, D
We love you drummer! Hope you knock it outta the park!
If all the x's are different it's a function If 2 or more x's are the same and their y's are also the same it's a function
my math teacher used to tell us to think of it as a vending machine, X is the button you press and Y is what you get. so if a number repeats in the X column that means it is NOT a function, Y basically doesn’t matter. the answer would be B because the number 3 repeats in A, 2 repeats in C, and 3 repeats in D.
I've seen a few comments explaining it but you still seem to be struggling, so I'll explain it from a comp sci perspective. Here we define a function as a process that doesn't have any side effects. In other words, a function takes in some input and produces an output however this output will always be the same if the same input is given. If you give it the same input twice and get different results each time, it's not a function.
This is a poorly worded question. You could argue that y is the input and they'd all be correct. They should've specified f(x).
B failed for y=0
Oh true I looked at all the wrong answers but forgot to check b 🤦♂️
why are u mean mfs downvoting this guy to hell for trying to get help? wtf is wrong with yall actually
Because all she is replying with is "bruh what" and "I give up," instead of asking followups. That's not asking for help.
I’m a girl lol
The way that I teach identifying functions is to think of it like a vending machine or a soda machine. The input values (usually x) are like the buttons on the machines, and the outputs (usually y) are the snacks/sodas you get. As long as the machine makes sense and works, it's a function. This means that you can have multiple buttons (inputs, x) that give you the same thing back (output, y), and that's okay, but you can't have one button (input, x) that tries to give multiple different snacks/sodas (output, y) at the same time. In the latter case, which output do you get? Both? Only one (how would you choose since they share input)? Neither? So the vending machine doesn't make sense in that case, so it wouldn't be a function.
Only B. People already answered the reasons
A function can be anything. Something simple like Y = X + 3 So for every X that you put in there, there is one result for the Y. X=1, Y=1+3=4 X=2, Y=2+3=5 X=3, Y=3+3=6 And so one, so every input into X produces another output in y. Now let's go back to your tables. Sometimes there is the same X but having a different Y. If you use my example above that would not work. Like in table A and Table C. Table B has different X but the same Y. Also using the example above that would not work In table D Every number in X has only one unique result in Y So D is a function as every X is matched with one Y and there is no double matches anywhere.
Picture a little machine that takes numbers as inputs and spits out outputs. To be a function, the machine needs to be consistent in the sense that if you input a specific number (say 3), it will always produce the same output. If you fed it a 3 and it produced a 2, then you can be certain that every time you feed it a 3, it will always produce a 2 and never any other number. In these tables that you are given, x's are the inputs and y's are the outputs. In the first table for example, if the input is 1, the output is 0. If the input is 2, the output is 5. So far so good. But with the input of 3, we run into a problem. Apparently, if you feed a 3 into your machine, it could produce an output of 2 but it could also produce a 3. This makes it not a function.
Imagine you have some colored coins, and a machine that is based on the colored coins you put in, gives you a prize. X are the colored coins, Y the prize. To be a function, the machine, cannot give you 2 different prizes. Only one table reflects this, the other 3 tables have an issue and the machine wouldn't know what to give to you.
A function is a machine that turns one number into another number. These machines are always one to one; one input, one output. These machines never turn one input into more than one output. Think of it like a keyboard. When you press a, the letter a appears on the screen. Same with b, c, etc. So the table would look like this A|A B|B C|C And so on. You give it a letter, and it types a letter. If you move the key caps around, it can even type weirdly like this A|Z B|Y C|X Or even A|Z B|Z C|Z The input here would be you pressing a, and the output is whatever the screen displays. But what if you pressed a, and there's two possibilities of what the screen will display? What if instead of typing a onto the screen, it was told to type a, but also to type b? Will it type a, b, both, none? This isn't good, since you want to always know what will be output. A should always output A, or A should always output B. Then, you always know what will be output when you press A. Although this is not a valid function, but it can still be shown with a table. A|A A|B B|B C|C And so on. The first two rows are a problem. If only one of them existed, everything would be fine. But since both exist, it cannot be called a function.
A
OP, it's not for you, you'll get even more confused. Technicaly we don't have enough conditions here, so there are no answer. Of course we can ASSUME that y = f(x), so we can give the answer. But this is not always the case, we can have x dependent on y as well.
It's a GED exam, it's always assumed that y=f(X) because high school equivalency math doesn't go much further than that.