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Nonlinear Functions

SAT Math· difficulty 4/5

For the polynomial f(x)=3x5−2x3+x−1f(x) = 3x^5 - 2x^3 + x - 1, what is the end behavior?

  • A

    As x→−∞x \to -\infty, f(x)→−∞f(x) \to -\infty; as x→+∞x \to +\infty, f(x)→+∞f(x) \to +\infty

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  • B

    As x→−∞x \to -\infty, f(x)→+∞f(x) \to +\infty; as x→+∞x \to +\infty, f(x)→−∞f(x) \to -\infty

  • C

    Both ends →−∞\to -\infty

  • D

    Both ends →+∞\to +\infty

Explanation

Odd degree (5) with positive leading coefficient (3): left end goes to −∞-\infty, right end goes to +∞+\infty.

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