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Is the function s(x)=−x4+8x3−9x2s(x) = -x^4 + 8x^3 - 9x^2 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither

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Q. Is the function s(x)=−x4+8x3−9x2s(x) = -x^4 + 8x^3 - 9x^2 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither
  1. Substitute −x-x in s(x)s(x): s(x)=−x4+8x3−9x2s(x) = -x^4 + 8x^3 - 9x^2\newlineFind s(−x)s(-x) by substituting −x-x for xx in s(x)s(x).\newlines(−x)=−(−x)4+8(−x)3−9(−x)2s(-x) = -(-x)^4 + 8(-x)^3 - 9(-x)^2
  2. Simplify s(−x)s(-x): s(−x)=−(−x)4+8(−x)3−9(−x)2s(-x) = -(-x)^4 + 8(-x)^3 - 9(-x)^2\newlineSimplify the right side of the function.\newlines(−x)=−x4−8x3−9x2s(-x) = -x^4 - 8x^3 - 9x^2
  3. Compare s(x)s(x) and s(−x)s(-x): Compare s(x)s(x) and s(−x)s(-x). We have s(x)=−x4+8x3−9x2s(x) = -x^4 + 8x^3 - 9x^2 and s(−x)=−x4−8x3−9x2s(-x) = -x^4 - 8x^3 - 9x^2. Since s(−x)≠s(x)s(-x) \neq s(x) and s(−x)≠−s(x)s(-x) \neq -s(x), s(x)s(x) is neither even nor odd.

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