Question

How do you determine if `f(x)=2x^3-9x` is an even or odd function?

Answer 1

odd function

Explanation:

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

• If a function is even then f(x) = f(- x) , for all x.

Even functions have symmetry about the y-axis.

• If a function is odd then - f(x) = f(-x) , for all x.

Odd functions have symmetry about the origin.

Test for even :

`f(-x) = 2(-x)^3 - 9(-x) = -2x^3 + 9x ≠ f(x)`
hence not even.

Test for odd :

`- f(x) = - (2x^3 - 9x ) = - 2x^3 + 9x = f(-x)`

Hence function is odd.

Here is the graph of the function- note symmetry about O.
graph{2x^3-9x [-20, 20, -10, 10]}