Question

is the function $k(x) = -4x^6 + 11x$ even, odd, or neither?
even \t odd \t neither
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Explanation:

Step1: Recall definitions

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

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

Given \( k(x) = -4x^6 + 11x \), substitute \( -x \) for \( x \):
\( k(-x) = -4(-x)^6 + 11(-x) \)
Simplify \( (-x)^6 = x^6 \) (since even power) and \( 11(-x) = -11x \):
\( k(-x) = -4x^6 - 11x \)

Step3: Compare with \( k(x) \) and \( -k(x) \)

• \( k(x) = -4x^6 + 11x \), so \( k(-x)

eq k(x) \) (not even).

• Compute \( -k(x) = -(-4x^6 + 11x) = 4x^6 - 11x \).

\( k(-x) = -4x^6 - 11x
eq 4x^6 - 11x = -k(x) \) (not odd).

Answer:

neither