Determine if the function is even, odd, or neither.
-$$f ( x ) = - 3 x ^ { 3 } + 5 x ^ { 2 } + 7$$
A) Odd
B) Even
C) Neither

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 all $x$ in the domain. For $f(x) = -3x^3 + 5x^2 + 7$, substituting $-x$ for $x$ gives $f(-x) = -3(-x)^3 + 5(-x)^2 + 7 = 3x^3 + 5x^2 + 7$, which is neither $f(x)$ nor $-f(x)$. Therefore, the function is neither even nor odd.

Determine If the Function Is Even, Odd, or Neither f(x)=−3x3+5x2+7f ( x ) = - 3 x ^ { 3 } + 5 x ^ { 2 } + 7f(x)=−3x3+5x2+7

Determine If the Function Is Even, Odd, or Neither $f ( x ) = - 3 x ^ { 3 } + 5 x ^ { 2 } + 7$