Questions: Describe the sequence of transformations that are required to graph g(x)=-5 sqrt(x-11)+12 based on f(x)=sqrt(x). The graph of f(x)=sqrt(x) is: - Shifted left 11 units - Stretched vertically by a factor of 5 - Reflected around the x-axis - Shifted up 12 units

Describe the sequence of transformations that are required to graph g(x)=-5 sqrt(x-11)+12 based on f(x)=sqrt(x). The graph of f(x)=sqrt(x) is: - Shifted left 11 units - Stretched vertically by a factor of 5 - Reflected around the x-axis - Shifted up 12 units
Transcript text: Describe the sequence of transformations that are required to graph $g(x)=-5 \sqrt{x-11}+12$ based on $f(x)=\sqrt{x}$. The graph of $f(x)=\sqrt{x}$ is: - Shifted left 11 units - Stretched vertically by a factor of 5 - Reflected around the $x$-axis - Shifted up 12 units
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Solution

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Solution Steps

Step 1: Horizontal Shift

The graph of $f(x) = \sqrt{x}$ is shifted 11 units to the right to obtain $h_1(x) = \sqrt{x-11}$.

Step 2: Vertical Stretch

The graph of $h_1(x)$ is stretched vertically by a factor of 5 to obtain $h_2(x) = 5\sqrt{x-11}$.

Step 3: Reflection

The graph of $h_2(x)$ is reflected across the x-axis to obtain $h_3(x) = -5\sqrt{x-11}$.

Step 4: Vertical Shift

The graph of $h_3(x)$ is shifted upwards by 12 units to obtain the graph of $g(x) = -5\sqrt{x-11} + 12$.

Final Answer

  1. Shift right 11 units.
  2. Stretch vertically by a factor of 5.
  3. Reflect across the x-axis.
  4. Shift up 12 units.
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