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

To check if a function is even or odd, we need to see if it satisfies the following properties for all $q$ in its domain:

1. $f(-q) = f(q)$ for even functions (even symmetry) 
2. $f(-q) = -f(q)$ for odd functions (odd symmetry)

Let's apply these properties to $f(q) = 2q^{3/2}$.

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

From 1, we see that $f(q)$ is not odd. From 2, we see that $f(q)$ is not even. Therefore, $f(q)$ is neither even nor odd.

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