Question

Determine algebraically if f(x)=x^2-8 is a function even, odd, or neither.

Answer 1

For a function to be even, it has to meet the following condition:

`f(x)=f(-x)`

To check if the given is an even function, evaluate the function at x and -x:

`\begin{gathered} f(x)=x^2-8 \\ f(-x)=(-x)^2-8=x^2-8 \\ f(x)=f(-x) \end{gathered}`

It means that the function is even.

For a function to be odd, it has to meet this condition:

`f(-x)=-f(x)`

We already know the values of f(-x) and f(x) and from this we can state that the function is not odd.