Write a piecewise function for each function graphed below. 12. 13. 14. Gina Wilson (All Things Algebra, LLC). 2015

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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### Piecewise Functions Worksheet

#### Problem 9

Given the piecewise function \( h(x) \):

\[ 
h(x) = 
  \begin{cases} 
   3x - 2 & \text{if } x < 0 \\
   -x + 1 & \text{if } x \geq 0 
  \end{cases} 
\]

- **Domain (D):** \_\_\_\_\_\_\_\_\_\_\_\_
- **Range (R):** \_\_\_\_\_\_\_\_\_\_\_\_

#### Problem 10

Given the piecewise function \( p(x) \):

\[
p(x) = 
  \begin{cases} 
   -3x + 7 & \text{if } x \leq 3 \\
   -x & \text{if } 3 < x < 5 \\
   -1 & \text{if } x \geq 5 
  \end{cases} 
\]

- **Domain (D):** \_\_\_\_\_\_\_\_\_\_\_\_
- **Range (R):** \_\_\_\_\_\_\_\_\_\_\_\_

#### Problem 11

Given the piecewise function \( k(x) \):

\[
k(x) = 
  \begin{cases} 
   x + 4 & \text{if } x < -1 \\
   5 & \text{if } -1 \leq x < 2 \\
   -\frac{1}{2}x + 1 & \text{if } x \geq 2 
  \end{cases} 
\]

- **Domain (D):** \_\_\_\_\_\_\_\_\_\_\_\_
- **Range (R):** \_\_\_\_\_\_\_\_\_\_\_\_

#### Graphs and Piecewise Function Description

**Problem 12**

- Graph has two sections:
  - A line with a closed dot at approximately (-3, 0) continuing straight through (0, 3) with an open dot at (3, 6).
  - Another line starting with a closed dot at (3, 6) and continuing upward.

**Problem 13**

- Graph has:
  - A downward sloping line with closed dot at (-3, 3
Transcribed Image Text:### Piecewise Functions Worksheet #### Problem 9 Given the piecewise function \( h(x) \): \[ h(x) = \begin{cases} 3x - 2 & \text{if } x < 0 \\ -x + 1 & \text{if } x \geq 0 \end{cases} \] - **Domain (D):** \_\_\_\_\_\_\_\_\_\_\_\_ - **Range (R):** \_\_\_\_\_\_\_\_\_\_\_\_ #### Problem 10 Given the piecewise function \( p(x) \): \[ p(x) = \begin{cases} -3x + 7 & \text{if } x \leq 3 \\ -x & \text{if } 3 < x < 5 \\ -1 & \text{if } x \geq 5 \end{cases} \] - **Domain (D):** \_\_\_\_\_\_\_\_\_\_\_\_ - **Range (R):** \_\_\_\_\_\_\_\_\_\_\_\_ #### Problem 11 Given the piecewise function \( k(x) \): \[ k(x) = \begin{cases} x + 4 & \text{if } x < -1 \\ 5 & \text{if } -1 \leq x < 2 \\ -\frac{1}{2}x + 1 & \text{if } x \geq 2 \end{cases} \] - **Domain (D):** \_\_\_\_\_\_\_\_\_\_\_\_ - **Range (R):** \_\_\_\_\_\_\_\_\_\_\_\_ #### Graphs and Piecewise Function Description **Problem 12** - Graph has two sections: - A line with a closed dot at approximately (-3, 0) continuing straight through (0, 3) with an open dot at (3, 6). - Another line starting with a closed dot at (3, 6) and continuing upward. **Problem 13** - Graph has: - A downward sloping line with closed dot at (-3, 3
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