How do you determine if #f(x)=2x^3-9x# is an even or odd function?
1 Answer
Mar 18, 2016
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]}
