Is the function q(x)=x^6-9 even, odd, or neither? Choices: [[even][odd][neither]]

Determining Function Type: To determine if the function q(x) is even, odd, or neither, we need to compare q(x) with q(-x). If q(x) = q(-x), then the function is even. If q(x) = -q(-x), then the function is odd. If neither condition is met, the function is neither even nor odd.Writing Down the Function: First, we write down the given function: q(x) = x^6 - 9.Finding q(-x): Next, we find q(-x) by substituting -x for x in the function: q(-x) = (-x)^6 - 9.Simplifying q(-x): We simplify q(-x). Since (-x)^6 = x^6 (because the exponent 6 is even), we get q(-x) = x^6 - 9.Comparing q(x) and q(-x): Now we compare q(x) with q(-x). We have q(x) = x^6 - 9 and q(-x) = x^6 - 9. Since q(x) = q(-x), the function q(x) is even.

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Is the function $q(x) = x^6 - 9$ even, odd, or neither? $\newline$ Choices: $\newline$ $\text{[[even][odd][neither]]}$

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Algebra 2

Even and odd functions

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Q. Is the function

q(x) = x^6 - 9

even, odd, or neither?

\newline

Choices:

\newline

\text{[[even][odd][neither]]}

Determining Function Type: To determine if the function $q(x)$ is even, odd, or neither, we need to compare $q(x)$ with $q(-x)$ . If $q(x) = q(-x)$ , then the function is even. If $q(x) = -q(-x)$ , then the function is odd. If neither condition is met, the function is neither even nor odd.
Writing Down the Function: First, we write down the given function: $q(x) = x^6 - 9$ .
Finding q(-x): Next, we find $q(-x)$ by substituting $-x$ for $x$ in the function: $q(-x) = (-x)^6 - 9$ .
Simplifying $q(-x)$ : We simplify $q(-x)$ . Since $(-x)^6 = x^6$ (because the exponent $6$ is even), we get $q(-x) = x^6 - 9$ .
Comparing $q(x)$ and $q(-x)$ : Now we compare $q(x)$ with $q(-x)$ . We have $q(x) = x^6 - 9$ and $q(-x) = (-x)^6 - 9$ . Since $q(x) = q(-x)$ , the function $q(x)$ is even.