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

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 ${y}^{2} = 4 , \therefore y = = \pm 2$. 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 $x = {\left(2\right)}^{2} - 2 = 4 - 2 = 2$

But for $y = - 2$ we have $x = {\left(- 2\right)}^{2} - 2 = 4 - 2 = 2$

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