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Use the graph off to sketch the graph of f1. Then use the graphs to determine the domain and range of each function. Choose the correct graph of the inverse function f ¹ below. O A. O B. G 1(+5,-5) O D. y=x Q

Use the graph off to sketch the graph of f1. Then use the graphs to determine the domain and range of each function. Choose the correct graph of the inverse function f ¹ below. O A. O B. G 1(+5,-5) O D. y=x Q

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Understanding Inverse Functions This educational activity focuses on using the graph of a function \( f \) to sketch the graph of its inverse \( f^{-1} \). Additionally, you will use these graphs to determine the domain and range of each function. #### Task 1. **Graph Analysis**: Use the given graph of \( f \) to sketch \( f^{-1} \). 2. **Domain and Range**: Determine the domain and range of both \( f \) and \( f^{-1} \) using the graphs. #### Provided Graph of \( f \) The graph of the function \( f \) is depicted in an xy-plane with the following key points: - \((-5, -5)\) - \((4, 1)\) - \((x, x)\) representing the line \( y = x \), the line of symmetry for a function and its inverse. - \((2, 3)\) - \((1, 2)\) The grid has a scale in both the x and y directions, with units marked from -7 to 7. #### Choosing the Correct Inverse Graph There are four options provided (A, B, C, and D). Your task is to identify which graph correctly depicts the inverse of the given function \( f \). **Option A**: - The graph appears as a reflection across the line \( y = x \) with key points swapped between x and y values of the given function \( f \). **Option B**: - Similar reflection to Option A but with possible differences in the connections between points. **Option C**: - Another possibility for \( f^{-1} \), though requires checking against the original graph points. **Option D**: - Also appears to reflect across the line \( y = x \) but with different configurations. ### Graph Explanation #### Provided Graph Details: - **Key Points**: Clearly labeled points are \((-5,-5)\), \((4,1)\), \((2,3)\), \((1,2)\). - **Line of Symmetry**: Line \( y = x \). Points on this line reflect for inverse functions. #### Inverse Graphs Analysis: Carefully reflect each given point and observe the changes in connections between points for each option: - If \( (a, b) \) is on \( f \), then \( (b, a) \
Transcribed Image Text:### Understanding Inverse Functions This educational activity focuses on using the graph of a function \( f \) to sketch the graph of its inverse \( f^{-1} \). Additionally, you will use these graphs to determine the domain and range of each function. #### Task 1. **Graph Analysis**: Use the given graph of \( f \) to sketch \( f^{-1} \). 2. **Domain and Range**: Determine the domain and range of both \( f \) and \( f^{-1} \) using the graphs. #### Provided Graph of \( f \) The graph of the function \( f \) is depicted in an xy-plane with the following key points: - \((-5, -5)\) - \((4, 1)\) - \((x, x)\) representing the line \( y = x \), the line of symmetry for a function and its inverse. - \((2, 3)\) - \((1, 2)\) The grid has a scale in both the x and y directions, with units marked from -7 to 7. #### Choosing the Correct Inverse Graph There are four options provided (A, B, C, and D). Your task is to identify which graph correctly depicts the inverse of the given function \( f \). **Option A**: - The graph appears as a reflection across the line \( y = x \) with key points swapped between x and y values of the given function \( f \). **Option B**: - Similar reflection to Option A but with possible differences in the connections between points. **Option C**: - Another possibility for \( f^{-1} \), though requires checking against the original graph points. **Option D**: - Also appears to reflect across the line \( y = x \) but with different configurations. ### Graph Explanation #### Provided Graph Details: - **Key Points**: Clearly labeled points are \((-5,-5)\), \((4,1)\), \((2,3)\), \((1,2)\). - **Line of Symmetry**: Line \( y = x \). Points on this line reflect for inverse functions. #### Inverse Graphs Analysis: Carefully reflect each given point and observe the changes in connections between points for each option: - If \( (a, b) \) is on \( f \), then \( (b, a) \
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