Question

How do you determine if `f(x)=-2x^3+8x` is an even or odd function?

Answer 1

odd function

Explanation:

To determine wether a function is odd/even, apply the following conditions.

• 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 if even function

f( -x) = `-2(-x)^3 + 8(-x) = 2x^3 - 8x ≠ f(x)`

`rArr " f(x) is not an even function "`

Test if odd function

`- f(x) = -(-2x^3 + 8x) = 2x^3 - 8x = f( -x)`

`rArr " f(x) is an odd function "`

This is the graph of f(x) . Note symmetry about O.
graph{-2x^3+8x [-20, 20, -10, 10]}