**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.
**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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde84ee81-4f35-40ff-a0b2-9d955f8c8854%2F650ca8c7-c70c-4899-a48e-e4b242f93e69%2F8bkcbsg.jpeg&w=3840&q=75)
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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