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Sketch a graph of ƒ(x) = 1 2x-1 -2 if x < -1 if −1 1

Sketch a graph of ƒ(x) = 1 2x-1 -2 if x < -1 if −1 1

Algebra and Trigonometry (6th Edition)
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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Sketch a graph of f(r)
### Piecewise Function Graphing Problem #### Question 9 Sketch a graph of \( f(x) = \begin{cases} 1 & \text{if } x \leq -1 \\ -2x - 1 & \text{if } -1 < x \leq 1 \\ -2 & \text{if } x > 1 \end{cases} \) #### Explanation: To sketch the graph of the piecewise function given, follow these steps for each case of the function: 1. **For \( x \leq -1 \):** - The function \( f(x) = 1 \). - This means for all \( x \) less than or equal to -1, \( f(x) \) will be a horizontal line at \( y = 1 \). 2. **For \(-1 < x \leq 1 \):** - The function \( f(x) = -2x - 1 \). - This is a linear function with a slope of -2 and a y-intercept at -1. - Plot this line from just right of \( x = -1 \) to \( x = 1 \). 3. **For \( x > 1 \):** - The function \( f(x) = -2 \). - This indicates a horizontal line at \( y = -2 \) for all \( x \) greater than 1. #### Graph Details: - The coordinate plane provided has the range marked from -5 to 5 on both the x and y axes. #### Steps to Plot: 1. **For \( x \leq -1 \):** - Locate the vertical line at \( x = -1 \). - Draw a horizontal line at \( y = 1 \) extending leftwards from \( x = -1 \). 2. **For \(-1 < x \leq 1 \):** - Find the point just right of \( x = -1 \). - Calculate \( f(x) \) at the boundary points: - At \( x = -1 \), \( f(x) = -2(-1) - 1 = 1 \). - At \( x = 1 \), \( f(x) = -2(1) - 1 = -3 \). - Connect these calculated boundary points
Transcribed Image Text:### Piecewise Function Graphing Problem #### Question 9 Sketch a graph of \( f(x) = \begin{cases} 1 & \text{if } x \leq -1 \\ -2x - 1 & \text{if } -1 < x \leq 1 \\ -2 & \text{if } x > 1 \end{cases} \) #### Explanation: To sketch the graph of the piecewise function given, follow these steps for each case of the function: 1. **For \( x \leq -1 \):** - The function \( f(x) = 1 \). - This means for all \( x \) less than or equal to -1, \( f(x) \) will be a horizontal line at \( y = 1 \). 2. **For \(-1 < x \leq 1 \):** - The function \( f(x) = -2x - 1 \). - This is a linear function with a slope of -2 and a y-intercept at -1. - Plot this line from just right of \( x = -1 \) to \( x = 1 \). 3. **For \( x > 1 \):** - The function \( f(x) = -2 \). - This indicates a horizontal line at \( y = -2 \) for all \( x \) greater than 1. #### Graph Details: - The coordinate plane provided has the range marked from -5 to 5 on both the x and y axes. #### Steps to Plot: 1. **For \( x \leq -1 \):** - Locate the vertical line at \( x = -1 \). - Draw a horizontal line at \( y = 1 \) extending leftwards from \( x = -1 \). 2. **For \(-1 < x \leq 1 \):** - Find the point just right of \( x = -1 \). - Calculate \( f(x) \) at the boundary points: - At \( x = -1 \), \( f(x) = -2(-1) - 1 = 1 \). - At \( x = 1 \), \( f(x) = -2(1) - 1 = -3 \). - Connect these calculated boundary points
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