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Which of the following set of piece-wise functions matches the graph shown? 3 if x<-3 if -3≤x≤3 2x-4 if x > 3 3 if x<-3 -x+2 if -3≤x≤3 -2x-2 if x > 2 a(x)=x+2 a. b. b(x)= = O -3 -2 -1 31 11 -11 -31 -4 c. c(x)=2x-1 d. d(x) = if if 2x-4 if 3 if -x+2 if 2x-4 if x <-3 -3≤x≤3 x > 3 x <3 5≤x≤-1 x > 2

Which of the following set of piece-wise functions matches the graph shown? 3 if x<-3 if -3≤x≤3 2x-4 if x > 3 3 if x<-3 -x+2 if -3≤x≤3 -2x-2 if x > 2 a(x)=x+2 a. b. b(x)= = O -3 -2 -1 31 11 -11 -31 -4 c. c(x)=2x-1 d. d(x) = if if 2x-4 if 3 if -x+2 if 2x-4 if x <-3 -3≤x≤3 x > 3 x <3 5≤x≤-1 x > 2

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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**Piece-wise Function Matching** **Question:** Which of the following set of piece-wise functions matches the graph shown? *Graph Explanation:* - The graph is a piece-wise function with three distinct sections. - For \( x < -3 \), the function value is a constant \( y = 3 \). - For \( -3 \leq x \leq 3 \), the function has a segment with a negative slope that passes through several points including \( (0, 2) \). - For \( x > 2 \), the function has a segment with a positive slope, starting from \( (3, -3) \). **Options:** a. \[ a(x) = \begin{cases} 3 & \text{if } x < -3 \\ -x + 2 & \text{if } -3 \le x \le 3 \\ 2x - 4 & \text{if } x > 3 \end{cases} \] b. \[ b(x) = \begin{cases} 3 & \text{if } x < -3 \\ -x + 2 & \text{if } -3 \le x \le 3 \\ -2x - 2 & \text{if } x > 2 \end{cases} \] c. \[ c(x) = \begin{cases} 3 & \text{if } x < -3 \\ 2x - 1 & \text{if } -3 \le x \le 3 \\ 2x - 4 & \text{if } x > 3 \end{cases} \] d. \[ d(x) = \begin{cases} 3 & \text{if } x < 3 \\ -x + 2 & \text{if } 5 \le x \le -1 \\ 2x - 4 & \text{if } x > 2 \end{cases} \] **Answer Explanation:** - The correct piece-wise function should correspond to the segments identified in the graph. - For the segment with \( x < -3 \), the value is \( 3 \). - For the segment between \( -3 \leq x \leq 3 \), the function \( -x + 2 \) fits as it passes through recognized
Transcribed Image Text:**Piece-wise Function Matching** **Question:** Which of the following set of piece-wise functions matches the graph shown? *Graph Explanation:* - The graph is a piece-wise function with three distinct sections. - For \( x < -3 \), the function value is a constant \( y = 3 \). - For \( -3 \leq x \leq 3 \), the function has a segment with a negative slope that passes through several points including \( (0, 2) \). - For \( x > 2 \), the function has a segment with a positive slope, starting from \( (3, -3) \). **Options:** a. \[ a(x) = \begin{cases} 3 & \text{if } x < -3 \\ -x + 2 & \text{if } -3 \le x \le 3 \\ 2x - 4 & \text{if } x > 3 \end{cases} \] b. \[ b(x) = \begin{cases} 3 & \text{if } x < -3 \\ -x + 2 & \text{if } -3 \le x \le 3 \\ -2x - 2 & \text{if } x > 2 \end{cases} \] c. \[ c(x) = \begin{cases} 3 & \text{if } x < -3 \\ 2x - 1 & \text{if } -3 \le x \le 3 \\ 2x - 4 & \text{if } x > 3 \end{cases} \] d. \[ d(x) = \begin{cases} 3 & \text{if } x < 3 \\ -x + 2 & \text{if } 5 \le x \le -1 \\ 2x - 4 & \text{if } x > 2 \end{cases} \] **Answer Explanation:** - The correct piece-wise function should correspond to the segments identified in the graph. - For the segment with \( x < -3 \), the value is \( 3 \). - For the segment between \( -3 \leq x \leq 3 \), the function \( -x + 2 \) fits as it passes through recognized
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