Determine whether the function is an even function, an odd function, or neither.
-$f ( x ) = x ^ { 3 } + x ^ { 2 } - 4$
A)Odd
B)Neither
C)Even

Question

Quizplus · Accepted Answer

A function is even if $f(-x) = f(x)$ for all $x$ in the domain, and odd if $f(-x) = -f(x)$. For $f(x) = x^3 + x^2 - 4$, $f(-x) = (-x)^3 + (-x)^2 - 4 = -x^3 + x^2 - 4$, which is neither $f(x)$ nor $-f(x)$. Therefore, the function is neither even nor odd.

Determine Whether the Function Is an Even Function, an Odd f(x)=x3+x2−4f ( x ) = x ^ { 3 } + x ^ { 2 } - 4f(x)=x3+x2−4

Determine Whether the Function Is an Even Function, an Odd $f ( x ) = x ^ { 3 } + x ^ { 2 } - 4$