Question

How do you determine if `k(x) = -2x^3` is an even or odd function?

Answer 1

odd function

Explanation:

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

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

Even functions are symmetrical about the y-axis.

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

Odd functions are symmetrical about the origin.

Test for even

`k(-x)=-2(-x)^3=2x^3≠k(x)`

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

Test for odd

`-k(x)=-(-2x^3)=2x^3=k(-x)`

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

Note symmetry about the origin in the graph
graph{-2x^3 [-10, 10, -5, 5]}