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Nonlinear Functions

SAT Math· difficulty 5/5

The graph of y=f(x)y = f(x) is transformed to y=−3f(2x−4)+5y = -3f(2x - 4) + 5. Which describes the transformation in correct order?

  • A

    Horizontal stretch 2, right 2, reflect, up 5

  • B

    Right 4, horizontal compression by 2, vertical stretch 3, up 5

  • C

    Horizontal compression by 2, right 4, vertical stretch 3, reflect xx-axis, up 5

  • D

    Horizontal compression by 2, right 2, vertical stretch 3, reflect xx-axis, up 5

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Explanation

Rewrite f(2x−4)=f(2(x−2))f(2x - 4) = f(2(x - 2)): horizontal compression by 2, then right 2. The factor −3-3: vertical stretch 3 then reflect over xx-axis. Finally up 5.

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