Question

How do you determine if `f(x)=-3x²+7` is an even or odd function?

Answer 1

even function

Explanation:

To determine if a function is even/odd the following applies.

• If f(x) = f( -x) , then function is even

Even functions are symmetrical about the y-axis.

• If f( -x) = - f(x) , then function is odd

Odd functions have symmetry about the origin.

Test for even

`f(-x)=-3(-x)^2+7=-3x^2+7=f(x)`

Since f(x) = f( -x) , then f(x) is an even function

Here is graph of f(x). Note symmetry about y-axis
graph{-3x^2+7 [-20, 20, -10, 10]}