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Nonlinear Functions

SAT Math· difficulty 4/5

What are the vertical and horizontal asymptotes of y=3x−6x+2y = \frac{3x - 6}{x + 2}?

  • A

    Vertical: x=2x = 2, Horizontal: y=3y = 3

  • B

    Vertical: x=−2x = -2, Horizontal: y=−6y = -6

  • C

    Vertical: x=3x = 3, Horizontal: y=−2y = -2

  • D

    Vertical: x=−2x = -2, Horizontal: y=3y = 3

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Explanation

Vertical: set x+2=0⇒x=−2x + 2 = 0 \Rightarrow x = -2. Horizontal: ratio of leading coefficients =31=3= \frac{3}{1} = 3.

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