Problem

Use transformations of the absolute value function, $f(x)=|x|$, to graph the function $h(x)=-|x-8|$.

What transformations are needed in order to obtain the graph of $h(x)$ from the graph of $f(x)$ ? Select all that apply.
A. Reflection about the $x$-axis
B. Horizontal stretch/shrink
C. Reflection about the $y$-axis
D. Horizontal shift
E. Vertical shift
F. Vertical stretch/shrink

Answer

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Answer

Final Answer: The transformations needed to obtain the graph of $h(x)$ from the graph of $f(x)$ are: \(\boxed{\text{A. Reflection about the x-axis}}\) and \(\boxed{\text{D. Horizontal shift}}\)

Steps

Step 1 :The function $h(x)=-|x-8|$ can be obtained from the function $f(x)=|x|$ by applying two transformations: a horizontal shift to the right by 8 units and a reflection about the x-axis.

Step 2 :The horizontal shift is represented by the '-8' inside the absolute value function. This shifts the graph of the function to the right by 8 units.

Step 3 :The reflection about the x-axis is represented by the negative sign in front of the absolute value function. This flips the graph of the function over the x-axis.

Step 4 :So, the correct answers are A and D.

Step 5 :Final Answer: The transformations needed to obtain the graph of $h(x)$ from the graph of $f(x)$ are: \(\boxed{\text{A. Reflection about the x-axis}}\) and \(\boxed{\text{D. Horizontal shift}}\)

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