Question

How do you determine if `y=2x^3 + 4x` is an even or odd function?

Answer 1

odd function

Explanation:

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

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

Even functions have symmetry 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)=2(-x)^3+4(-x)=-2x^3-4x≠f(x)`

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

Test for odd

`-f(x)=-(2x^3+4x)=-2x^3-4x=f(-x)`

Since f( -x) = - f(x) , then f(x) is odd

Note symmetry about origin in graph.
graph{2x^3+4x [-40, 40, -20, 20]}