Question

is the function $w(x) = -2x^{5}+7x^{2}$ even, odd, or neither?
even
odd
neither
submit

Explanation:

Step1: Recall even/odd function rules

A function is even if $w(-x) = w(x)$, odd if $w(-x) = -w(x)$.

Step2: Compute $w(-x)$

$$\begin{align*} w(-x) &= -2(-x)^5 + 7(-x)^2\\ &= -2(-x^5) + 7(x^2)\\ &= 2x^5 + 7x^2 \end{align*}$$

Step3: Compare to $w(x)$ and $-w(x)$

Original $w(x) = -2x^5 + 7x^2$, and $-w(x) = 2x^5 - 7x^2$.
$w(-x)
eq w(x)$ and $w(-x)
eq -w(x)$.

Answer:

neither