Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![### Piecewise Function Analysis
The image contains a piecewise function graph and its corresponding function rules.
#### Graph Details:
- **Sections:**
- The graph is divided into three segments based on different intervals of \( x \).
- **Segment 1**:
- **Interval**: \(-6 \leq x \leq -1\)
- Solid dot at \((-6, 2)\) and open dot at \((-1, 5)\).
- Linearly increases from \( y = 2 \) to \( y = 5 \).
- **Segment 2**:
- **Interval**: \(-1 < x \leq 3\)
- Horizontal line at \( y = 4 \) between \( x = -1 \) and \( x = 3 \).
- **Segment 3**:
- **Interval**: \(3 < x \leq 6\)
- Solid dot at \((3, 3)\) and \((6, -2)\), with the line decreasing linearly.
- **Endpoints**:
- Solid dots indicate the point is included in the interval.
- Open dots indicate the point is not included in the interval.
#### Function Notation:
\[
f(x) =
\begin{cases}
\text{Enter the function rule} & \text{if } -6 \leq x \leq -1 \\
4 & \text{if } -1 < x \leq 3 \\
\text{Enter the function rule} & \text{if } 3 < x \leq 6
\end{cases}
\]
- The function rules for the intervals \(-6 \leq x \leq -1\) and \(3 < x \leq 6\) need to be determined based on the slopes of the lines in the graph.
This analysis helps students understand how to interpret and write piecewise functions based on graph segments.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79384b4f-f6f5-4976-8d61-12e63a60eeb0%2F9476da2b-cf7d-4dc7-b215-d98b8f1ffa46%2Feabgbgu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Piecewise Function Analysis
The image contains a piecewise function graph and its corresponding function rules.
#### Graph Details:
- **Sections:**
- The graph is divided into three segments based on different intervals of \( x \).
- **Segment 1**:
- **Interval**: \(-6 \leq x \leq -1\)
- Solid dot at \((-6, 2)\) and open dot at \((-1, 5)\).
- Linearly increases from \( y = 2 \) to \( y = 5 \).
- **Segment 2**:
- **Interval**: \(-1 < x \leq 3\)
- Horizontal line at \( y = 4 \) between \( x = -1 \) and \( x = 3 \).
- **Segment 3**:
- **Interval**: \(3 < x \leq 6\)
- Solid dot at \((3, 3)\) and \((6, -2)\), with the line decreasing linearly.
- **Endpoints**:
- Solid dots indicate the point is included in the interval.
- Open dots indicate the point is not included in the interval.
#### Function Notation:
\[
f(x) =
\begin{cases}
\text{Enter the function rule} & \text{if } -6 \leq x \leq -1 \\
4 & \text{if } -1 < x \leq 3 \\
\text{Enter the function rule} & \text{if } 3 < x \leq 6
\end{cases}
\]
- The function rules for the intervals \(-6 \leq x \leq -1\) and \(3 < x \leq 6\) need to be determined based on the slopes of the lines in the graph.
This analysis helps students understand how to interpret and write piecewise functions based on graph segments.
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