Question

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

Answer 1

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.

Answer 2

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