Questions: Use transformations of the absolute value function, f(x)=x, to graph the function h(x)=x-2+3. 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 y-axis B. Vertical stretch/shrink C. Horizontal shift D. Reflection about the x-axis E. Vertical shift F. Horizontal stretch/shrink

Use transformations of the absolute value function, f(x)=x, to graph the function h(x)=x-2+3.

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 y-axis B. Vertical stretch/shrink C. Horizontal shift D. Reflection about the x-axis E. Vertical shift F. Horizontal stretch/shrink

Transcript text: Part 1 of 2 Use transformations of the absolute value function, $f(x)=|x|$, to graph the function $h(x)=|x-2|+3$. 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 $y$-axis B. Vertical stretch/shrink C. Horizontal shift D. Reflection about the $x$-axis E. Vertical shift F. Horizontal stretch/shrink

Solution

Solution Steps

Step 1: Identify the transformations

To obtain the graph of $ h(x) = |x-2| + 3 $ from the graph of $ f(x) = |x| $, we need to identify the transformations applied to $ f(x) $.

Step 2: Horizontal shift

The term $ |x-2| $ indicates a horizontal shift. Specifically, it is a shift to the right by 2 units.

Step 3: Vertical shift

The term $ +3 $ indicates a vertical shift. Specifically, it is a shift upwards by 3 units.

Final Answer

The transformations needed are: C. Horizontal shift E. Vertical shift

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 5, "ymin": -1, "ymax": 10}, "commands": ["y = abs(x)", "y = abs(x-2) + 3"], "latex_expressions": ["$f(x) = |x|$", "$h(x) = |x-2| + 3$"]}

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