Functions

[alioop]

I do not know how to test if an equation is or is not a function. my two problems right now are 1. x=y^2-4 and 2. y=x^2-4

 

[pka]

I do not know how to test if an equation is or is not a function. my two problems right now are 1. x=y^2-4 and 2. y=x^2-4

Functions are sets of ordered \(\displaystyle (x,y)\). No two pairs may have the same first term.
This is known as the vertical line test: no vertical line may cut the graph of a function more than once.

The pairs \(\displaystyle (0,2)~\&~(0,-2)\) belong to the graph of \(\displaystyle x=y^2-4\). So can it be an function?

 

[HallsofIvy]

When you are asked to determine whether or not something is a "function", the first thing you should do is look at the definition of "function"! A "function" is a set of ordered pairs, {(x, y)} so that no two different pairs have the same x value. If two pairs had both x and y the same, they would not be "different" so we are looking for situations where the same "y" can be given by two different values of x. The there are such, this is NOT a function If there are not two x y pairs with the same y but different x, that is a function.