Question

reflecting the cubic function practice
complete this assessment to review what youve learned. it wil
what type of function is $f(x) = -5x^3$?
option #1: even
option #2: odd
option #3: neither
(1 point)

Explanation:

Step1: Recall definitions of even/odd functions

An even function satisfies \( f(-x) = f(x) \), an odd function satisfies \( f(-x) = -f(x) \).

Step2: Compute \( f(-x) \) for \( f(x) = -5x^3 \)

Substitute \( -x \) into \( f(x) \): \( f(-x) = -5(-x)^3 \). Simplify \( (-x)^3 = -x^3 \), so \( f(-x) = -5(-x^3) = 5x^3 \).

Step3: Compare \( f(-x) \) with \( -f(x) \)

Compute \( -f(x) = -(-5x^3) = 5x^3 \). Since \( f(-x) = -f(x) \), the function is odd.

Answer:

Option #2: odd