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Nonlinear Functions

SAT Math· difficulty 5/5

What is the horizontal asymptote of y=ex−1ex+1y = \frac{e^x - 1}{e^x + 1} as x→∞x \to \infty?

  • A

    y=ey = e

  • B

    y=−1y = -1

  • C

    y=1y = 1

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  • D

    y=0y = 0

Explanation

As x→∞x \to \infty, divide top and bottom by exe^x: 1−e−x1+e−x→11=1\frac{1 - e^{-x}}{1 + e^{-x}} \to \frac{1}{1} = 1.

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