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Is the function q(x)=−4x4−3x3q(x) = -4x^4 - 3x^3 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither

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Full solution

Q. Is the function q(x)=−4x4−3x3q(x) = -4x^4 - 3x^3 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither
  1. Plug in −x-x: Plug in −x-x for xx in the function to find q(−x)q(-x).\newlineq(−x)=−4(−x)4−3(−x)3q(-x) = -4(-x)^4 - 3(-x)^3
  2. Simplify q(−x)q(-x): Simplify the function q(−x)q(-x).q(−x)=−4x4+3x3q(-x) = -4x^4 + 3x^3
  3. Compare q(x)q(x) and q(−x)q(-x): Compare q(x)q(x) and q(−x)q(-x).
    q(x)=−4x4−3x3q(x) = -4x^4 - 3x^3
    q(−x)=−4x4+3x3q(-x) = -4x^4 + 3x^3
    Since q(−x)≠q(x)q(-x) \neq q(x) and q(−x)≠−q(x)q(-x) \neq -q(x), the function is neither even nor odd.

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