is the function s(x) = 5x^7 + 2x^3 - 9x even, odd, or neither? even odd neither

Explanation:

Step1: Recall function - type rules

An even function satisfies $s(-x)=s(x)$ and an odd function satisfies $s(-x)=-s(x)$.

Step2: Find $s(-x)$

Substitute $-x$ into $s(x)=5x^{7}+2x^{3}-9x$. We get $s(-x)=5(-x)^{7}+2(-x)^{3}-9(-x)$.

Step3: Simplify $s(-x)$

Using the rule that $(-a)^{n}=-a^{n}$ when $n$ is odd, $s(-x)=-5x^{7}-2x^{3}+9x =-(5x^{7}+2x^{3}-9x)$.

Step4: Compare with $s(x)$

Since $s(-x)=-s(x)$, the function is odd.

Answer:

odd