# Graphing a Piecewise-Defined Function ## Introduction to Piecewise-Defined Functions In this activity, we will explore how to graph a piecewise-defined function. A piecewise-defined function is a function that is defined by different expressions for different intervals of the domain. ### Function Definition Suppose the function \( h \) is defined as follows: \[ h(x) = \begin{cases} -1 & \text{if } -1.5 < x \leq -0.5 \\ 0 & \text{if } -0.5 < x \leq 0.5 \\ 1 & \text{if } 0.5 < x \leq 1.5 \\ 2 & \text{if } 1.5 \leq x < 2.5 \\ 3 & \text{if } 2.5 \leq x < 3.5 \end{cases} \] ### Graph Description The graph of the function \( h \) consists of horizontal line segments corresponding to each interval of \( x \): 1. **Interval \(-1.5 < x \leq -0.5\):** - The function value is \( -1 \). - The graph displays a horizontal line at \( y = -1 \) between \( x = -1.5 \) and \( x = -0.5 \). 2. **Interval \(-0.5 < x \leq 0.5\):** - The function value is \( 0 \). - The graph is a horizontal line at \( y = 0 \) from \( x = -0.5 \) to \( x = 0.5 \). 3. **Interval \(0.5 < x \leq 1.5\):** - The function value is \( 1 \). - The horizontal line is at \( y = 1 \) for this interval. 4. **Interval \(1.5 \leq x < 2.5\):** - The function value is \( 2 \). - The line extends horizontally at \( y = 2 \) from \( x = 1.5 \) to \( x = 2.5 \). 5. **Interval \(2.5 \leq x <
# Graphing a Piecewise-Defined Function ## Introduction to Piecewise-Defined Functions In this activity, we will explore how to graph a piecewise-defined function. A piecewise-defined function is a function that is defined by different expressions for different intervals of the domain. ### Function Definition Suppose the function \( h \) is defined as follows: \[ h(x) = \begin{cases} -1 & \text{if } -1.5 < x \leq -0.5 \\ 0 & \text{if } -0.5 < x \leq 0.5 \\ 1 & \text{if } 0.5 < x \leq 1.5 \\ 2 & \text{if } 1.5 \leq x < 2.5 \\ 3 & \text{if } 2.5 \leq x < 3.5 \end{cases} \] ### Graph Description The graph of the function \( h \) consists of horizontal line segments corresponding to each interval of \( x \): 1. **Interval \(-1.5 < x \leq -0.5\):** - The function value is \( -1 \). - The graph displays a horizontal line at \( y = -1 \) between \( x = -1.5 \) and \( x = -0.5 \). 2. **Interval \(-0.5 < x \leq 0.5\):** - The function value is \( 0 \). - The graph is a horizontal line at \( y = 0 \) from \( x = -0.5 \) to \( x = 0.5 \). 3. **Interval \(0.5 < x \leq 1.5\):** - The function value is \( 1 \). - The horizontal line is at \( y = 1 \) for this interval. 4. **Interval \(1.5 \leq x < 2.5\):** - The function value is \( 2 \). - The line extends horizontally at \( y = 2 \) from \( x = 1.5 \) to \( x = 2.5 \). 5. **Interval \(2.5 \leq x <
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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![# Graphing a Piecewise-Defined Function
## Introduction to Piecewise-Defined Functions
In this activity, we will explore how to graph a piecewise-defined function. A piecewise-defined function is a function that is defined by different expressions for different intervals of the domain.
### Function Definition
Suppose the function \( h \) is defined as follows:
\[
h(x) =
\begin{cases}
-1 & \text{if } -1.5 < x \leq -0.5 \\
0 & \text{if } -0.5 < x \leq 0.5 \\
1 & \text{if } 0.5 < x \leq 1.5 \\
2 & \text{if } 1.5 \leq x < 2.5 \\
3 & \text{if } 2.5 \leq x < 3.5
\end{cases}
\]
### Graph Description
The graph of the function \( h \) consists of horizontal line segments corresponding to each interval of \( x \):
1. **Interval \(-1.5 < x \leq -0.5\):**
- The function value is \( -1 \).
- The graph displays a horizontal line at \( y = -1 \) between \( x = -1.5 \) and \( x = -0.5 \).
2. **Interval \(-0.5 < x \leq 0.5\):**
- The function value is \( 0 \).
- The graph is a horizontal line at \( y = 0 \) from \( x = -0.5 \) to \( x = 0.5 \).
3. **Interval \(0.5 < x \leq 1.5\):**
- The function value is \( 1 \).
- The horizontal line is at \( y = 1 \) for this interval.
4. **Interval \(1.5 \leq x < 2.5\):**
- The function value is \( 2 \).
- The line extends horizontally at \( y = 2 \) from \( x = 1.5 \) to \( x = 2.5 \).
5. **Interval \(2.5 \leq x <](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F831fad36-dc94-48af-9172-e5010521abec%2Fdf507989-a03c-46b7-aa3b-d5d467ebbb3c%2Fgukj3mt.jpeg&w=3840&q=75)
Transcribed Image Text:# Graphing a Piecewise-Defined Function
## Introduction to Piecewise-Defined Functions
In this activity, we will explore how to graph a piecewise-defined function. A piecewise-defined function is a function that is defined by different expressions for different intervals of the domain.
### Function Definition
Suppose the function \( h \) is defined as follows:
\[
h(x) =
\begin{cases}
-1 & \text{if } -1.5 < x \leq -0.5 \\
0 & \text{if } -0.5 < x \leq 0.5 \\
1 & \text{if } 0.5 < x \leq 1.5 \\
2 & \text{if } 1.5 \leq x < 2.5 \\
3 & \text{if } 2.5 \leq x < 3.5
\end{cases}
\]
### Graph Description
The graph of the function \( h \) consists of horizontal line segments corresponding to each interval of \( x \):
1. **Interval \(-1.5 < x \leq -0.5\):**
- The function value is \( -1 \).
- The graph displays a horizontal line at \( y = -1 \) between \( x = -1.5 \) and \( x = -0.5 \).
2. **Interval \(-0.5 < x \leq 0.5\):**
- The function value is \( 0 \).
- The graph is a horizontal line at \( y = 0 \) from \( x = -0.5 \) to \( x = 0.5 \).
3. **Interval \(0.5 < x \leq 1.5\):**
- The function value is \( 1 \).
- The horizontal line is at \( y = 1 \) for this interval.
4. **Interval \(1.5 \leq x < 2.5\):**
- The function value is \( 2 \).
- The line extends horizontally at \( y = 2 \) from \( x = 1.5 \) to \( x = 2.5 \).
5. **Interval \(2.5 \leq x <
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