Is the function p(x) = 5x^3 - 2x + 11 even, odd, or neither? Choices: (A)even (B)odd (C)neither

Calculate p(-x): Calculate p(-x) by substituting -x for x in p(x) = 5x^3 - 2x + 11. p(-x) = 5(-x)^3 - 2(-x) + 11Simplify p(-x): Simplify p(-x). p(-x) = -5x^3 + 2x + 11Compare p(x) and p(-x): Compare p(x) and p(-x). We have p(x) = 5x^3 - 2x + 11 and p(-x) = -5x^3 + 2x + 11. Since p(-x) ≠ p(x) and p(-x) ≠ -p(x), p(x) is neither even nor odd.

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Is the function $p(x) = 5x^3 - 2x + 11$ 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

p(x) = 5x^3 - 2x + 11

even, odd, or neither?

\newline

Choices:

\newline

(A)even

\newline

(B)odd

\newline

(C)neither

Calculate $p(-x)$ : Calculate $p(-x)$ by substituting $-x$ for $x$ in $p(x) = 5x^3 - 2x + 11$ . $\newline$ $p(-x) = 5(-x)^3 - 2(-x) + 11$
Simplify $p(-x)$ : Simplify $p(-x)$ . $p(-x) = -5x^3 + 2x + 11$
Compare $p(x)$ and $p(-x)$ : Compare $p(x)$ and $p(-x)$ . We have $p(x) = 5x^3 - 2x + 11$ and $p(-x) = -5x^3 + 2x + 11$ . Since $p(-x) \neq p(x)$ and $p(-x) \neq -p(x)$ , $p(x)$ is neither even nor odd.