Use the graph to evaluate the following expressions: a. f(3) = 2.5 ]• Preview b. f-'(2) = 2.5 Preview %3D c. f-'(– 2) = 2.5 Preview d. f-'(f( – 2)) = 2/5 Preview e. f-(f(351)) = -1/351 Preview f(f-'(7)) = F7 Preview

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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I solved the first few problems but I can't seem to figure the rest of the questions. I'm not sure if I'm reading the graph incorrectly

**Graph Analysis and Function Evaluation**

In this lesson, we explore a linear graph of a function \( f \). The provided graph can be interacted with for a better understanding of how the function behaves.

### Graph Description:
- The graph displays a straight blue line with an upward slope, intersecting the y-axis at \( y = -2 \).
- The x-axis ranges from -4 to 4, and the y-axis ranges from -8 to 8.
- The graph represents a linear function, likely in the form \( y = mx + b \).

### Evaluation Using the Graph:
Using the graph, we can find the values of the function \( f(x) \) for specific x-values and determine the inverse function \( f^{-1}(y) \) for given y-values.

#### Expressions:
- **a.** \( f(3) = 2.5 \)  
  The function value at \( x = 3 \) is correctly evaluated as 2.5.
  
- **b.** \( f^{-1}(2) = 2.5 \)  
  The x-value corresponding to \( y = 2 \) is correctly identified as 2.5.

- **c.** \( f^{-1}(-2) = -2.5 \)  
  The x-value corresponding to \( y = -2 \) is incorrectly evaluated. Check the line's y-intercept for correction.

- **d.** \( f^{-1}(f(-2)) = 2/5 \)  
  Incorrect evaluation—determine \( f(-2) \) first, then find \( f^{-1} \).

- **e.** \( f^{-1}(f(351)) = -1/351 \)  
  Incorrect—find \( f(351) \) and then its \( f^{-1} \).

- **f.** \( f(f^{-1}(7)) = -7 \)  
  Incorrect—evaluate \( f^{-1}(7) \) and then apply \( f \).

### Conclusion:
This exercise helps in understanding the evaluation of functions and their inverses using a graphical approach. Reassess incorrect calculations and utilize graph interaction for improved comprehension and accuracy.
Transcribed Image Text:**Graph Analysis and Function Evaluation** In this lesson, we explore a linear graph of a function \( f \). The provided graph can be interacted with for a better understanding of how the function behaves. ### Graph Description: - The graph displays a straight blue line with an upward slope, intersecting the y-axis at \( y = -2 \). - The x-axis ranges from -4 to 4, and the y-axis ranges from -8 to 8. - The graph represents a linear function, likely in the form \( y = mx + b \). ### Evaluation Using the Graph: Using the graph, we can find the values of the function \( f(x) \) for specific x-values and determine the inverse function \( f^{-1}(y) \) for given y-values. #### Expressions: - **a.** \( f(3) = 2.5 \) The function value at \( x = 3 \) is correctly evaluated as 2.5. - **b.** \( f^{-1}(2) = 2.5 \) The x-value corresponding to \( y = 2 \) is correctly identified as 2.5. - **c.** \( f^{-1}(-2) = -2.5 \) The x-value corresponding to \( y = -2 \) is incorrectly evaluated. Check the line's y-intercept for correction. - **d.** \( f^{-1}(f(-2)) = 2/5 \) Incorrect evaluation—determine \( f(-2) \) first, then find \( f^{-1} \). - **e.** \( f^{-1}(f(351)) = -1/351 \) Incorrect—find \( f(351) \) and then its \( f^{-1} \). - **f.** \( f(f^{-1}(7)) = -7 \) Incorrect—evaluate \( f^{-1}(7) \) and then apply \( f \). ### Conclusion: This exercise helps in understanding the evaluation of functions and their inverses using a graphical approach. Reassess incorrect calculations and utilize graph interaction for improved comprehension and accuracy.
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