**Graph Explanation** The graph displayed shows a V-shaped plot typical of an absolute value function. The original function is given as \( f(x) = |x| \), and the graph is a transformation of this function. - **Axes and Grid**: The graph is plotted on a standard Cartesian coordinate grid with x and y axes. The x-axis ranges from -6 to 6, while the y-axis ranges from -5 to 5. - **Function Behavior**: The vertex of the graph appears to be at (-2, 0), indicating a horizontal shift to the left by 2 units of the basic absolute value function \( f(x) = |x| \). **Question and Task** The graph above is a transformation of the function \( f(x) = |x| \). Write an equation for the function graphed above: \[ g(x) = \_\_\_\_\_ \] **Guide** Based on the described transformation, the equation for the transformed function could be expressed as \( g(x) = |x + 2| \). **Additional Help** If you need further assistance, you can reach out by clicking on "Message instructor." **Action Button** - **Submit Question**: Click here to submit your answer.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Graph Explanation**

The graph displayed shows a V-shaped plot typical of an absolute value function. The original function is given as \( f(x) = |x| \), and the graph is a transformation of this function.

- **Axes and Grid**: The graph is plotted on a standard Cartesian coordinate grid with x and y axes. The x-axis ranges from -6 to 6, while the y-axis ranges from -5 to 5.

- **Function Behavior**: The vertex of the graph appears to be at (-2, 0), indicating a horizontal shift to the left by 2 units of the basic absolute value function \( f(x) = |x| \).

**Question and Task**

The graph above is a transformation of the function \( f(x) = |x| \).

Write an equation for the function graphed above:

\[ g(x) = \_\_\_\_\_ \]

**Guide**

Based on the described transformation, the equation for the transformed function could be expressed as \( g(x) = |x + 2| \).

**Additional Help**

If you need further assistance, you can reach out by clicking on "Message instructor."

**Action Button**

- **Submit Question**: Click here to submit your answer.
Transcribed Image Text:**Graph Explanation** The graph displayed shows a V-shaped plot typical of an absolute value function. The original function is given as \( f(x) = |x| \), and the graph is a transformation of this function. - **Axes and Grid**: The graph is plotted on a standard Cartesian coordinate grid with x and y axes. The x-axis ranges from -6 to 6, while the y-axis ranges from -5 to 5. - **Function Behavior**: The vertex of the graph appears to be at (-2, 0), indicating a horizontal shift to the left by 2 units of the basic absolute value function \( f(x) = |x| \). **Question and Task** The graph above is a transformation of the function \( f(x) = |x| \). Write an equation for the function graphed above: \[ g(x) = \_\_\_\_\_ \] **Guide** Based on the described transformation, the equation for the transformed function could be expressed as \( g(x) = |x + 2| \). **Additional Help** If you need further assistance, you can reach out by clicking on "Message instructor." **Action Button** - **Submit Question**: Click here to submit your answer.
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