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Nonlinear Functions

SAT Math· difficulty 3/5

For the polynomial f(x)=−2x4+3x2−7f(x) = -2x^4 + 3x^2 - 7, what is the end behavior?

  • A

    As x→±∞x \to \pm\infty, f(x)→+∞f(x) \to +\infty

  • B

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

  • C

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

  • D

    As x→±∞x \to \pm\infty, f(x)→−∞f(x) \to -\infty

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Explanation

Leading term −2x4-2x^4: even degree with negative coefficient means both ends go to −∞-\infty.

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