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Nonlinear Functions

SAT Math· difficulty 4/5

A graph of an exponential function has horizontal asymptote y=3y = 3 and passes through (0,5)(0, 5). Which equation matches?

  • A

    y=5⋅2xy = 5 \cdot 2^x

  • B

    y=2⋅2x+3y = 2 \cdot 2^x + 3

  • C

    y=2x+3y = 2^x + 3

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  • D

    y=3⋅2xy = 3 \cdot 2^x

Explanation

Asymptote at 3 means +3+3. At x=0x = 0: 20+3=42^0 + 3 = 4 — wait, check options: 20+3=4≠52^0 + 3 = 4 \neq 5. Reconsider: y=2⋅2x+3y = 2 \cdot 2^x + 3: at x=0x = 0, y=2+3=5y = 2 + 3 = 5. Choose option A.

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