Questions: Use transformations of the absolute value function, f(x)=x, to graph the function h(x)=x-2-7. What transformations are needed in order to obtain the graph of h(x) from the graph of f(x) ? Select all that apply. A. Horizontal stretch/shrink B. Vertical shift C. Reflection about the y-axis D. Reflection about the x-axis E. Horizontal shift F. Vertical stretch/shrink

Use transformations of the absolute value function, f(x)=x, to graph the function h(x)=x-2-7. What transformations are needed in order to obtain the graph of h(x) from the graph of f(x) ? Select all that apply. A. Horizontal stretch/shrink B. Vertical shift C. Reflection about the y-axis D. Reflection about the x-axis E. Horizontal shift F. Vertical stretch/shrink
Transcript text: Use transformations of the absolute value function, $f(x)=|x|$, to graph the function $h(x)=|x-2|-7$. What transformations are needed in order to obtain the graph of $h(x)$ from the graph of $f(x)$ ? Select all that apply. A. Horizontal stretch/shrink B. Vertical shift C. Reflection about the $y$-axis D. Reflection about the $x$-axis E. Horizontal shift F. Vertical stretch/shrink
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Solution

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Solution Steps

Step 1: Identify the base function

The base function given is \( f(x) = |x| \).

Step 2: Analyze the given function

The function to graph is \( h(x) = |x - 2| - 7 \).

Step 3: Determine the transformations
  • The term \( |x - 2| \) indicates a horizontal shift to the right by 2 units.
  • The term \( -7 \) indicates a vertical shift downward by 7 units.

Final Answer

The transformations needed are:

  • Horizontal shift (E)
  • Vertical shift (B)
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