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# 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.

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• 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
• 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.
• Respect the website. It's a great one!
• Is it ever possible to have a function that has two (or more) values assigned to one element on the y axis?
• This is possible, but the function would not have an inverse. You'll find out about these in a later video.
• 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
• 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!
• Could you switch the axes, i.e. make the vertical line y and make the horizontal line f(y)?
• 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.
• 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?
• 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.
• 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.
• 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.
• Why is the f(x) axis f(x) and not f(y) since it would be the y-axis on a normal coordinate plane?
• 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.
• 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
• 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.