Algebraically determine whether the function below is even, odd, or neither.
$f ( q ) = 2 q ^ { 3 / 2 }$
A) even
B) odd
C) cannot be determined
D) neither

Question

Quizplus · Accepted Answer

A function is even if $f(-x)=f(x)$ for all $x$ in the domain. 
A function is odd if $f(-x)=-f(x)$ for all $x$ in the domain.

For $f(q)=2q^{3/2}$, we have:

$f(-q)=2(-q)^{3/2}=-2q^{3/2}$

However,

$-f(q)=-2q^{3/2}$

Since $f(-q)=-f(x)$ $= -f(q)$, the function is neither even nor odd.

Algebraically Determine Whether the Function Below Is Even, Odd, or Neither