if x < -2 Sketch a graph of f(x) = x-1 if -2 1 Note: Be sure to include closed or open dots, but only at breaks in the graph. -5 -4 -3 -2 -1 5+ 4 3 2 1 -1 -2- -3 -N 2 3 4
if x < -2 Sketch a graph of f(x) = x-1 if -2 1 Note: Be sure to include closed or open dots, but only at breaks in the graph. -5 -4 -3 -2 -1 5+ 4 3 2 1 -1 -2- -3 -N 2 3 4
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 Function Graphing Tutorial
#### Problem Statement
**Sketch a graph of \( f(x) \):**
\[
f(x) =
\begin{cases}
-3 & \text{if } x \leq -2 \\
x - 1 & \text{if } -2 < x \leq 1 \\
-3 & \text{if } x > 1
\end{cases}
\]
**Note**: Be sure to include closed or open dots, but only at breaks in the graph.
#### Graphing Instructions
1. **Graph the first piece**:
For \( x \leq -2 \), the function \( f(x) = -3 \).
- Draw a horizontal line at \( y = -3 \) for \( x \leq -2 \).
- Place a closed dot at \( (-2, -3) \).
2. **Graph the second piece**:
For \( -2 < x \leq 1 \), the function \( f(x) = x - 1 \).
- This is a linear function. Plot the line segment starting just after \( x = -2 \) and ending at \( x = 1 \).
- Place an open dot at \( (-2, -3) \).
- Since \( f(x) = x - 1 \), at \( x = -2 \), \( f(x) = -3 \),
- At \( x = 1 \), \( f(x) = 0 \), place a closed dot at \( (1, 0) \).
3. **Graph the third piece**:
For \( x > 1 \), the function \( f(x) = -3 \).
- Draw a horizontal line at \( y = -3 \) for \( x > 1 \).
- Place an open dot at \( (1, -3) \).
#### Explanation of the Graph Layout
- **Axes**: The x-axis ranges from -5 to 5 and the y-axis ranges from -5 to 5.
- **Detailed Steps**:
- Plot horizontal line at \( y = -3 \) from \( x = -5 \) to \( x = -2 \) with a closed dot at \( (-2, -3) \).
- Plot the linear segment from just after \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec5383c7-ce71-4639-9c19-f5515f12eee5%2F76e1c182-377c-4d9e-9a5f-23c61c11ed26%2Faiqg63_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Piecewise Function Graphing Tutorial
#### Problem Statement
**Sketch a graph of \( f(x) \):**
\[
f(x) =
\begin{cases}
-3 & \text{if } x \leq -2 \\
x - 1 & \text{if } -2 < x \leq 1 \\
-3 & \text{if } x > 1
\end{cases}
\]
**Note**: Be sure to include closed or open dots, but only at breaks in the graph.
#### Graphing Instructions
1. **Graph the first piece**:
For \( x \leq -2 \), the function \( f(x) = -3 \).
- Draw a horizontal line at \( y = -3 \) for \( x \leq -2 \).
- Place a closed dot at \( (-2, -3) \).
2. **Graph the second piece**:
For \( -2 < x \leq 1 \), the function \( f(x) = x - 1 \).
- This is a linear function. Plot the line segment starting just after \( x = -2 \) and ending at \( x = 1 \).
- Place an open dot at \( (-2, -3) \).
- Since \( f(x) = x - 1 \), at \( x = -2 \), \( f(x) = -3 \),
- At \( x = 1 \), \( f(x) = 0 \), place a closed dot at \( (1, 0) \).
3. **Graph the third piece**:
For \( x > 1 \), the function \( f(x) = -3 \).
- Draw a horizontal line at \( y = -3 \) for \( x > 1 \).
- Place an open dot at \( (1, -3) \).
#### Explanation of the Graph Layout
- **Axes**: The x-axis ranges from -5 to 5 and the y-axis ranges from -5 to 5.
- **Detailed Steps**:
- Plot horizontal line at \( y = -3 \) from \( x = -5 \) to \( x = -2 \) with a closed dot at \( (-2, -3) \).
- Plot the linear segment from just after \(
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