Main content

## 8th grade

### Course: 8th grade > Unit 3

Lesson 12: Recognizing functions- Testing if a relationship is a function
- Relations and functions
- Recognizing functions from graph
- Checking if a table represents a function
- Recognize functions from tables
- Recognizing functions from table
- Checking if an equation represents a function
- Does a vertical line represent a function?
- Recognize functions from graphs
- Recognizing functions from verbal description
- Recognizing functions from verbal description word problem

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Testing if a relationship is a function

Learn to determine if points on a graph represent a function. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- if this were a quadraic funcion there would be 2 outputs for each input , is a quadratic function a special type of fuction that is immune to these rules(69 votes)
- A "C" graph would have a single X value that would output 2 Y values. The vertical line test fails and therefore it would not be a function. A quadratic or "U" function outputs a single Y value for every X value. This graph passes the vertical line test and is therefore a function.(13 votes)

- Is it ever possible to have a function that has two (or more) values assigned to one element on the y axis?(6 votes)
- This is possible, but the function would not have an inverse. You'll find out about these in a later video.(8 votes)

- Respect the website. It's a great one!(10 votes)
- I rely on subtitles, so I'm guessing as to what this video is about, but I believe the video was talking about how a function cannot have multiple y values for any given x value. Have I understood this correctly?(5 votes)
- The Y axis can't be on the X axisbecause it is just the vention they both have to stay on the lines or sides.(2 votes)

- Could you switch the axes, i.e. make the vertical line y and make the horizontal line f(y)?(3 votes)
- It is not as standard, but you do see that from time to time, particularly in calculus problems in which one representation is simpler than the other.(7 votes)

- A WAY easier (and faster), way to know if it is a function is to see if there are two of the same x-intercept (which make a vertical line). If there is, then it is NOT a function. Hope that answered any of your stated ?'s and to-be ?'s. Sorry if that doesn't though, I try.(5 votes)
- Another way you can tell if it is a function is if it sticks to the y=mx+b formula. Such as if I had a slope (m) of 3 and a y intercept (b) of -1, every point would have to stick to that formula.(2 votes)

- Hey

I get you can't have 2 numbers in range for 1 in domain (e.g. 1,6. 1,9)

But can you call it a function if its (2,-3) (2,3) (3,4) (3,-4). You know what I mean. Like the same number except in negative and positive(2 votes)- Sid, that's a good question! That would
**not**be a function, because you can't have the same domain give you different ranges. Here's the way I think of it: basically, "Multiple domains can have the same range, but one domain cannot have multiple ranges".

Hope that helps!(8 votes)

- Why is the f(x) axis f(x) and not f(y) since it would be the y-axis on a normal coordinate plane?(4 votes)
- f(x)=y. In a function, f(x) means "the function of x". For example, f(x)=2x is the same thing as y=2x. But f(y) would be something different entirely, because that would be using the function definition to change the y-value.(4 votes)

- So a function can have 2 inputs for 1 output like in quadratics, but can't have 2 outputs for 1 input? y=x^2 is a function but x=y^2 isn't. Is there any reasoning behind this? Thanks(4 votes)
- If y is a function of x, there must be at most one output for any given x. That makes sense, because the value of y depends only on x.

If y can take on more than one value for any given value of x, then there must be some additional factor that determines the output. So in this case, y is not a function of x, it is a function of x and something else.(3 votes)

- I get that f(4) is not a function but does the graph still represent a function?(2 votes)
- Phew. That was the only doubt I had in the entire functions module. Thank you hkapur97. :)(1 vote)

## Video transcript

We're asked: Do the points
on the graph below represent a function? So in order for the points to
represent a function, for every input into our function,
we can only get one value. So if we look here, they've
graphed the point--it looks like negative 1, 3, so that's
the point negative 1, 3. So if we assume that this is our
x-axis and that is our f of x axis, and I'm just assuming
it's a function, I don't know whether it really
is just now, this point is telling us that if you put
negative 1 into our function, or that thing that might be
a function, or maybe our relation, you'll get a 3 So
it's telling us that f of negative 1 is equal to 3. So far it could be a reasonable
function. You give me negative 1 and
I will map it to 3. Then they have if x is 2, then
our value is negative 2. This is the point 2, negative
2, so that still seems consistent with being
a function. If you pass me 2, I will map
you or I will point you to negative 2. Seems fair enough. Let's see this next
value here. This is the point 3 comma
2 right there. So once again, that says that,
look, if you give me 3 into my function, into my black box,
I will output a 2. Pretty reasonable. No reason why these points
can't represent a function so far. Now, what about when we input
4 into the function? Let me do this in magenta. So what happens if I input
4 into my function? So this is 4 right here. Well, according to these points,
there's two points that relate to 4 that
4 can be mapped to. I could map it to the
point 4 comma 5. So that says if you give me
a 4, I'll give you a 5. But it also says if you give me
a 4, I could also give you a negative 1 because that's
the point 4, negative 1 So this is not a function. It cannot be a function if for
some input into the function you could give me two
different values. And you can see that
right here. And an easy test is to just
see, look, for one value I have two points for
this relationship. So this cannot be a function. So this is not a function! I'll put an exclamation mark.