How do you determine if #y=2x^3 + 4x# is an even or odd function?
1 Answer
Jun 4, 2016
odd function
Explanation:
To determine if a function is even/odd consider the following.
• 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 for even
#f(-x)=2(-x)^3+4(-x)=-2x^3-4x≠f(x)# Since f(x) ≠ f( -x) , then f(x) is not even.
Test for odd
#-f(x)=-(2x^3+4x)=-2x^3-4x=f(-x)# Since f( -x) = - f(x) , then f(x) is odd
Note symmetry about origin in graph.
graph{2x^3+4x [-40, 40, -20, 20]}