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Nonlinear Functions

SAT Math· difficulty 5/5

The graph of gg is the graph of ff shifted left 3, vertically compressed by a factor of 12\frac{1}{2}, and reflected over the xx-axis. Which is g(x)g(x) in terms of ff?

  • A

    g(x)=−12f(x−3)g(x) = -\frac{1}{2} f(x - 3)

  • B

    g(x)=12f(x+3)g(x) = \frac{1}{2} f(x + 3)

  • C

    g(x)=−2f(x+3)g(x) = -2 f(x + 3)

  • D

    g(x)=−12f(x+3)g(x) = -\frac{1}{2} f(x + 3)

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Explanation

Left 3: f(x+3)f(x + 3). Vertical compression by 12\frac{1}{2}: 12f(x+3)\frac{1}{2} f(x + 3). Reflect over xx-axis: −12f(x+3)-\frac{1}{2} f(x + 3).

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