Question

determine whether the function is odd, even, or neither.
$f(x) = x^5 + 2x^3 + 3x$
select one:
○ a. even and odd
○ b. even
○ c. odd
○ d. neither

Explanation:

Step1: Define $f(-x)$

Substitute $x$ with $-x$ in $f(x)$:
$f(-x) = (-x)^5 + 2(-x)^3 + 3(-x)$

Step2: Simplify each term

Apply exponent rules for negative bases:
$f(-x) = -x^5 - 2x^3 - 3x$

Step3: Factor out -1

Rewrite to compare with $-f(x)$:
$f(-x) = -(x^5 + 2x^3 + 3x) = -f(x)$

Answer:

C. Odd