Question

How do you determine if `f(x) = x^4 - x^3` is an even or odd function?

Answer 1

neither

Explanation:

To determine 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 symmetry about the origin.

Test for even

`f(-x)=(-x)^4-(-x)^3=x^4-(-x^3)=x^4+x^3`

Since f(x) ≠ f( -x) , then f(x) is not even

Test for odd

`-f(x)=-(x^4-x^3)=-x^4+x^3`

Since f( -x) ≠ - f(x) , then f(x) is not odd
graph{x^4-x^3 [-10, 10, -5, 5]}