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 just need question 10
![### Piecewise Functions and Graphing
This educational resource focuses on piecewise functions and their graphical representations. It includes examples, practice problems, and graphs to illustrate how piecewise functions are defined and interpreted.
#### Example Problems
**9. Function \( h(x) \):**
\[
h(x) =
\begin{cases}
\frac{4}{3}x - 2 & \text{if } x < 0 \\
-x + 1 & \text{if } x \geq 0
\end{cases}
\]
- **D =** (Domain)
- **R =** (Range)
**10. Function \( p(x) \):**
\[
p(x) =
\begin{cases}
-3x + 7 & \text{if } x \leq 3 \\
x & \text{if } 3 < x < 5 \\
-1 & \text{if } x \geq 5
\end{cases}
\]
- **D =** (Domain)
- **R =** (Range)
**11. Function \( k(x) \):**
\[
k(x) =
\begin{cases}
x + 4 & \text{if } x < -1 \\
5 & \text{if } -1 \leq x < 2 \\
-\frac{1}{2}x + 1 & \text{if } x \geq 2
\end{cases}
\]
- **D =** (Domain)
- **R =** (Range)
#### Graphs
- Each function is accompanied by an empty graph grid provided for students to plot the piecewise functions.
- These grids are structured with Cartesian coordinates (x and y-axes) marked along the edges. Arrows indicate positive direction for both axes.
#### Exercises
Below the example problems, there is a set of empty graph grids for students to practice graphing additional piecewise functions. Each grid is meant to foster understanding and strengthen skills in interpreting and sketching piecewise-defined functions.
This section emphasizes understanding the specific conditions under which each piece of the function applies and visualizing the transitions between different pieces.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61a624e8-9805-4882-bd7c-8b439f9ba0a9%2F84adb251-4396-4cbc-99d7-b86712db923f%2Fpqc0rx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Piecewise Functions and Graphing
This educational resource focuses on piecewise functions and their graphical representations. It includes examples, practice problems, and graphs to illustrate how piecewise functions are defined and interpreted.
#### Example Problems
**9. Function \( h(x) \):**
\[
h(x) =
\begin{cases}
\frac{4}{3}x - 2 & \text{if } x < 0 \\
-x + 1 & \text{if } x \geq 0
\end{cases}
\]
- **D =** (Domain)
- **R =** (Range)
**10. Function \( p(x) \):**
\[
p(x) =
\begin{cases}
-3x + 7 & \text{if } x \leq 3 \\
x & \text{if } 3 < x < 5 \\
-1 & \text{if } x \geq 5
\end{cases}
\]
- **D =** (Domain)
- **R =** (Range)
**11. Function \( k(x) \):**
\[
k(x) =
\begin{cases}
x + 4 & \text{if } x < -1 \\
5 & \text{if } -1 \leq x < 2 \\
-\frac{1}{2}x + 1 & \text{if } x \geq 2
\end{cases}
\]
- **D =** (Domain)
- **R =** (Range)
#### Graphs
- Each function is accompanied by an empty graph grid provided for students to plot the piecewise functions.
- These grids are structured with Cartesian coordinates (x and y-axes) marked along the edges. Arrows indicate positive direction for both axes.
#### Exercises
Below the example problems, there is a set of empty graph grids for students to practice graphing additional piecewise functions. Each grid is meant to foster understanding and strengthen skills in interpreting and sketching piecewise-defined functions.
This section emphasizes understanding the specific conditions under which each piece of the function applies and visualizing the transitions between different pieces.
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