Question

Determine algebraically if the function is odd, even, or neither:
f(x)=3x^5/2
I know to plug a -x in for x, but how do the exponents change?

Answer 1

f(-x)=3(-x)^5/2
when you raise a negative to an odd power it stays negative, so the expression will be -3x^5/2, which is not identical to f(x), so it's not even. HOWEVER, f(-x) = -f(x) so the function is ODD>

Answer 2

Thanks, I was never good at exponent rules, but this helped me remember :)