Questions: The functions f(x) and g(x) are shown on the graph. f(x)=x What is g(x) ? Text description for graph A. g(x)=x+1 B. g(x)=x+4 C. g(x)=x-4 D. g(x)=x-4

The functions f(x) and g(x) are shown on the graph. f(x)=x What is g(x) ? Text description for graph A. g(x)=x+1 B. g(x)=x+4 C. g(x)=x-4 D. g(x)=x-4
Transcript text: The functions $f(x)$ and $g(x)$ are shown on the graph. \[ f(x)=|x| \] What is $g(x)$ ? Text description for graph A. $g(x)=\left|x+\frac{4}{4}\right|$ B. $g(x)=|x|+4$ C. $g(x)=|x|-4$ D. $g(x)=|x-4|$ SUBMIT
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Solution

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Solution Steps

Step 1: Identify the given function

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

Step 2: Analyze the transformation

The graph of \( g(x) \) is a vertical shift of the graph of \( f(x) \). The graph of \( g(x) \) is shifted downward by 4 units compared to \( f(x) \).

Step 3: Determine the equation of \( g(x) \)

Since \( g(x) \) is a vertical shift of \( f(x) \) downward by 4 units, the equation of \( g(x) \) is \( g(x) = |x| - 4 \).

Final Answer

The correct option is: C. \( g(x) = |x| - 4 \)

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