How do you determine if #x^3-5# is an even or odd function?
1 Answer
Mar 20, 2016
neither
Explanation:
To determine if a function is even/odd the following applies.
• If the function is even then f(x) = f(-x), for all x
Even functions have symmetry about the y-axis
• If the function is odd then f(-x) = - f(x), for all x
Odd functions have symmetry about the origin
Test for even :
f(-x)
# = (-x)^3 - 5 = - x^3 - 5 ≠# f(x) hence not evenTest for odd :
# - f(x) = - (x^3 - 5) = - x^3 + 5 ≠ f (- x)" hence not odd " # The function
# x^3 - 5 " is neither even nor odd " #