Question

is the function r(x) = 2x⁴ - 16x² + 8x even, odd, or neither?
even
odd
neither

Explanation:

Step1: Recall the definitions

A function \( f(x) \) is even if \( f(-x) = f(x) \) for all \( x \) in the domain. A function \( f(x) \) is odd if \( f(-x) = -f(x) \) for all \( x \) in the domain.

Step2: Compute \( r(-x) \)

Given \( r(x)=2x^{4}-6x^{2}+8x \), substitute \( -x \) for \( x \):

$$
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Step3: Compare \( r(-x) \) with \( r(x) \) and \( -r(x) \)

• \( r(x)=2x^{4}-6x^{2}+8x \), \( r(-x)=2x^{4}-6x^{2}-8x \). Since \( r(-x)

eq r(x) \), the function is not even.

• Compute \( -r(x) \): \( -r(x)=-2x^{4}+6x^{2}-8x \). Since \( r(-x)

eq -r(x) \), the function is not odd.

Answer:

neither