Questions: Use transformations of the absolute value function, f(x)=x, to graph the function g(x)=-x-4+2 What transformations are needed in order to obtain the graph of g(x) from the graph of f(x)? Select all that apply. A. Reflection about the x-axis B. Reflection about the y-axis C. Horizontal stretch/shrink D. Vertical shift E. Vertical stretch/shrink F. Horizontal shift

Use transformations of the absolute value function, f(x)=x, to graph the function g(x)=-x-4+2

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

Transcript text: Use transformations of the absolute value function, $f(x)=|x|$, to graph the function $g(x)=-|x-4|+2$ What transformations are needed in order to obtain the graph of $g(x)$ from the graph of $f(x)$ ? Select all that apply. A. Reflection about the $x$-axis B. Reflection about the $y$-axis C. Horizontal stretch/shrink D. Vertical shift E. Vertical stretch/shrink F. Horizontal shift

Solution

Solution Steps

Step 1: Identify the base function

The base function is $ f(x) = |x| $.

Step 2: Analyze the transformation to $ g(x) $

The function $ g(x) = -|x-4|+2 $ can be obtained from $ f(x) = |x| $ through the following transformations:

Horizontal shift: The term $ x-4 $ indicates a shift to the right by 4 units.
Reflection about the $ x $-axis: The negative sign in front of the absolute value indicates a reflection over the $ x $-axis.
Vertical shift: The $ +2 $ indicates a shift upwards by 2 units.

Final Answer

The transformations needed are:

A. Reflection about the $ x $-axis
D. Vertical shift
F. Horizontal shift

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = -abs(x-4) + 2"], "latex_expressions": ["$y = -|x-4| + 2$"]}

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