Question

How do you determine if `f(x) = 5x^2` is an even or odd function?

Answer 1

f(x) is even

Explanation:

To determine, algebraically, if a function is even/odd consider the following.

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

Even functions are symmetrical about the y-axis.

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

Odd functions have half-turn symmetry about the origin.

Test for even

`f(-x)=5(-x)^2=5x^2=f(x)`

Since f(x) = f( -x) , then f(x) is even.
graph{5x^2 [-10, 10, -5, 5]}