Questions: Graphing Transformations of Absolute Value Functions The graph f(x)=x is shown below. Let g(x)=2f(x). Draw the graph of g(x) and write its formula below. Clear All Draw: Write the formula for g(x) below. Be sure to use proper function notation.

Graphing Transformations of Absolute Value Functions
The graph f(x)=x is shown below. Let g(x)=2f(x). Draw the graph of g(x) and write its formula below.
Clear All
Draw:

Write the formula for g(x) below. Be sure to use proper function notation.

Transcript text: Graphing Transformations of Absolute Value Functions The graph $f(x)=|x|$ is shown below. Let $g(x)=2 f(x)$. Draw the graph of $g(x)$ and write its formula below. Clear All Draw: $\square$ Write the formula for $g(x)$ below. Be sure to use proper function notation. $\square$

Solution

Solution Steps

Step 1: Analyze the transformation

The given function is $g(x) = 2f(x)$, where $f(x) = |x|$. This means $g(x) = 2|x|$. The transformation is a vertical stretch by a factor of 2.

Step 2: Apply the transformation

To graph $g(x) = 2|x|$, we take the graph of $f(x) = |x|$ and multiply the y-coordinate of each point by 2. For example, the point (1, 1) on the graph of $f(x)$ becomes (1, 2) on the graph of $g(x)$. Similarly, the point (-1, 1) becomes (-1, 2). The point (0, 0) remains at (0, 0).

Step 3: Draw the graph

The graph of $g(x) = 2|x|$ will be a "V" shape with a vertex at the origin (0, 0), but steeper than the graph of $f(x) = |x|$. The graph passes through the points (1, 2), (-1, 2), (2, 4), (-2, 4), and so on.

Final Answer

The formula for $g(x)$ is $g(x) = 2|x|$. The graph of $g(x)$ is a vertically stretched version of the graph of $f(x)$ by a factor of 2. \$ \boxed{g(x) = 2|x|} \$

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