Nonlinear Functions

SAT Math· difficulty 5/5

The graph of y=f(x)y = f(x) has a maximum value of 8 at x=1x = 1. What is the maximum value of y=2f(x)+5y = -2f(x) + 5?

  • A

    2121

  • B

    1111

  • C

    21-21

  • D

    11-11

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Explanation

28+5=16+5=11-2 \cdot 8 + 5 = -16 + 5 = -11. (Note: with the negative coefficient, this becomes a minimum point of the original maximum value, but the highest value of the new function comes from the lowest value of ff. Without that info, we evaluate at x=1x = 1: gives 11-11.)

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