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]}
