How do you determine if #f(x) = x^4 - x^3# is an even or odd function?
1 Answer
May 10, 2016
neither
Explanation:
To determine if a function is even/odd consider the following.
• If f(x) = f(-x) , then f(x) is even
Even functions are symmetrical 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)=(-x)^4-(-x)^3=x^4-(-x^3)=x^4+x^3# Since f(x) ≠ f( -x) , then f(x) is not even
Test for odd
#-f(x)=-(x^4-x^3)=-x^4+x^3# Since f( -x) ≠ - f(x) , then f(x) is not odd
graph{x^4-x^3 [-10, 10, -5, 5]}