is the functiom f(x) = -x^3 + 5x even, odd or neither?

Question

how can you tell if a function is even or odd or neither?

Answer 1

All odd degree polynomial functions are odd.

Answer 2

f(x) = -x³ + 5x

 

A function y = f(x) is odd if f(-x) = -f(x).

 

f(-x) = -(-x)³ + 5(-x) = x³ - 5x

 

                              = -f(x)

 

So, the given function is odd.  

 

NOTE:  It is NOT true that every odd degree polynomial function is odd.  

 

           For example, if g(x) = x³ + x + 2, then g(-x) ≠ -g(x).