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

1 Answer
Apr 13, 2016

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]}