Is the function r(x) = 2x^4 - 6x^2 + 8x even, odd, or neither? Choices: (A)even (B)odd (C)neither

Check even function: Check if r(x) is even by substituting -x for x and comparing r(-x) to r(x). r(-x) = 2(-x)^4 - 6(-x)^2 + 8(-x)Simplify r(-x): Simplify the expression for r(-x). r(-x) = 2x^4 - 6x^2 - 8xCompare r(-x) with r(x): Compare r(-x) with r(x). r(x) = 2x^4 - 6x^2 + 8x r(-x) = 2x^4 - 6x^2 - 8x Since r(-x) ≠ r(x), r(x) is not even.Check odd function: Check if r(x) is odd by checking if r(-x) = -r(x). -r(x) = -2x^4 + 6x^2 - 8xCompare -r(x) with r(-x): Compare -r(x) with r(-x). -r(x) = -2x^4 + 6x^2 - 8x r(-x) = 2x^4 - 6x^2 - 8x Since -r(x) ≠ r(-x), r(x) is not odd.Conclude function type: Conclude whether r(x) is even, odd, or neither. Since r(x) is neither even nor odd, the correct choice is (C) neither.

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Even and odd functions

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Q. Is the function

r(x) = 2x^4 - 6x^2 + 8x

even, odd, or neither?

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Choices:

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(A)even

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(B)odd

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(C)neither

Check even function: Check if $r(x)$ is even by substituting $-x$ for $x$ and comparing $r(-x)$ to $r(x)$ . $r(-x) = 2(-x)^4 - 6(-x)^2 + 8(-x)$
Simplify $r(-x)$ : Simplify the expression for $r(-x)$ . $r(-x) = 2x^4 - 6x^2 - 8x$
Compare $r(-x)$ with $r(x)$ : Compare $r(-x)$ with $r(x)$ .
$r(x) = 2x^4 - 6x^2 + 8x$
$r(-x) = 2x^4 - 6x^2 - 8x$
Since $r(-x) \neq r(x)$ , $r(x)$ is not even.
Check odd function: Check if $r(x)$ is odd by checking if $r(-x) = -r(x)$ . $-r(x) = -2x^4 + 6x^2 - 8x$
Compare $-r(x)$ with $r(-x)$ : Compare $-r(x)$ with $r(-x)$ .
$-r(x) = -2x^4 + 6x^2 - 8x$
$r(-x) = 2x^4 - 6x^2 - 8x$
Since $-r(x) \neq r(-x)$ , $r(x)$ is not odd.
Conclude function type: Conclude whether $r(x)$ is even, odd, or neither. Since $r(x)$ is neither even nor odd, the correct choice is (C) neither.