Is #x=y^2-2# a function?

2 Answers
Jul 9, 2018

No.

Explanation:

Because of a function's definition is that for any single #y# value, there exist one and only one #x# value. Here if we put in #x=2#, we get #y^2=4,:.y==+-2#. So, this indicates that this equation is not a function.

On the other hand, if you graph this, you can do the vertical line test. If you draw a vertical line and it intersects the equation more than once, then that equation does not represent a function.

Jul 9, 2018

NO. See below

Explanation:

A function is an aplication for which every single value of y, there is a single and only value of x.

Notice that for #y=2#, the relations gives #x=(2)^2-2=4-2=2#

But for #y=-2# we have #x=(-2)^2-2=4-2=2#

So, there are two values (2 and -2), for which the "function" gives the same value 2. Then it is not a function