Determine algebraically whether the function is even, odd, or neither even nor odd.
-$$f ( x ) = - 5 x ^ { 3 } + 3 x$$
A) Even
B) Neither
C) Odd

Name: Determine algebraically whether the function is even, odd, or neither even nor odd. -\[f ( x ) = - 5 x ^ { 3 } + 3 x\] A) Even B) Neither C) Odd
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Question

Quizplus · Accepted Answer

A function is odd if $f(-x) = -f(x)$ for all $x$ in the domain of $f$. For $f(x) = -5x^3 + 3x$, $f(-x) = -5(-x)^3 + 3(-x) = 5x^3 - 3x = -( -5x^3 + 3x ) = -f(x)$, which confirms $f(x)$ is odd.

Determine Algebraically Whether the Function Is Even, Odd, or Neither f(x)=−5x3+3xf ( x ) = - 5 x ^ { 3 } + 3 xf(x)=−5x3+3x

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