Is the function h(x) = x^3 + 2x even, odd, or neither? Choices: (A)even (B)odd (C)neither

Check Even Function: Check if h(x) is even by substituting -x for x and comparing h(-x) to h(x). h(-x) = (-x)^3 + 2(-x) h(-x) = -x^3 - 2xCompare h(-x) with h(x): Compare h(-x) with h(x). h(x) = x^3 + 2x h(-x) = -x^3 - 2x Since h(-x) ≠ h(x), h(x) is not even.Check Odd Function: Check if h(x) is odd by seeing if h(-x) = -h(x). h(-x) = -x^3 - 2x -h(x) = -(x^3 + 2x) -h(x) = -x^3 - 2x Since h(-x) = -h(x), h(x) is odd.

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Is the function $h(x) = x^3 + 2x$ even, odd, or neither? $\newline$ Choices: $\newline$ (A)even $\newline$ (B)odd $\newline$ (C)neither

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Algebra 2

Even and odd functions

Full solution

Q. Is the function

h(x) = x^3 + 2x

even, odd, or neither?

\newline

Choices:

\newline

(A)even

\newline

(B)odd

\newline

(C)neither

Check Even Function: Check if $h(x)$ is even by substituting $-x$ for $x$ and comparing $h(-x)$ to $h(x)$ .
$h(-x) = (-x)^3 + 2(-x)$
$h(-x) = -x^3 - 2x$
Compare $h(-x)$ with $h(x)$ : Compare $h(-x)$ with $h(x)$ . $h(x) = x^3 + 2x$ $h(-x) = -x^3 - 2x$ Since $h(-x) \neq h(x)$ , $h(x)$ is not even.
Check Odd Function: Check if $h(x)$ is odd by seeing if $h(-x) = -h(x)$ .
$h(-x) = -x^3 - 2x$
$-h(x) = -(x^3 + 2x)$
$-h(x) = -x^3 - 2x$
Since $h(-x) = -h(x)$ , $h(x)$ is odd.