Sketch a graph of f(x) 5 4 3 2 1 -5 -4 -3 -2 -1 - 1 { 0 if x ≤ - 2 x + 1 if -2 < x ≤ 2 if x > 2 2 3 4 5 Open Dot -1 -2 -3 -4 -5+ Clear All Draw: Line Dot
Sketch a graph of f(x) 5 4 3 2 1 -5 -4 -3 -2 -1 - 1 { 0 if x ≤ - 2 x + 1 if -2 < x ≤ 2 if x > 2 2 3 4 5 Open Dot -1 -2 -3 -4 -5+ Clear All Draw: Line Dot
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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![# Graphing a Piecewise Function
## Objective:
To sketch a graph of the piecewise function \( f(x) \) defined as follows:
\[
f(x) =
\begin{cases}
-1 & \text{if } x \leq -2 \\
x + 1 & \text{if } -2 < x \leq 2 \\
0 & \text{if } x > 2
\end{cases}
\]
## Steps to Sketch the Graph:
1. **For \( x \leq -2 \), \( f(x) = -1 \):**
- This part of the function is a constant value of -1 for all \( x \) values less than or equal to -2.
- Draw a horizontal line at \( y = -1 \) from the left end of the graph to \( x = -2 \).
- Include a closed dot at \( (-2, -1) \) since \( x = -2 \) is included in this interval.
2. **For \( -2 < x \leq 2 \), \( f(x) = x + 1 \):**
- This part of the function is a linear function with a slope of 1 and a y-intercept at \((0, 1)\).
- Draw a line starting just to the right of \( x = -2 \), which would begin at approximately \( (-2, -1+1 = -1) \).
- This line continues up to \( x = 2 \) and ends at \( y = 3 \) with a closed dot at \( (2, 3) \).
3. **For \( x > 2 \), \( f(x) = 0 \):**
- This part of the function is a constant value of 0 for all \( x \) values greater than 2.
- Draw a horizontal line at \( y = 0 \) starting from right after \( x = 2 \) towards the right end of the graph.
- Include an open dot at \( (2, 0) \) since \( x = 2 \) is not included in this interval.
## Graph Axes and Scale:
- The x-axis ranges from -5 to 5.
- The y-axis ranges from -5 to 5.
- The graph is drawn on a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc94e4e1c-3d4e-4486-b985-b30353acec86%2Fef664b71-e25a-44c6-aa6c-281a4dd80aeb%2Fgnpa32_processed.png&w=3840&q=75)
Transcribed Image Text:# Graphing a Piecewise Function
## Objective:
To sketch a graph of the piecewise function \( f(x) \) defined as follows:
\[
f(x) =
\begin{cases}
-1 & \text{if } x \leq -2 \\
x + 1 & \text{if } -2 < x \leq 2 \\
0 & \text{if } x > 2
\end{cases}
\]
## Steps to Sketch the Graph:
1. **For \( x \leq -2 \), \( f(x) = -1 \):**
- This part of the function is a constant value of -1 for all \( x \) values less than or equal to -2.
- Draw a horizontal line at \( y = -1 \) from the left end of the graph to \( x = -2 \).
- Include a closed dot at \( (-2, -1) \) since \( x = -2 \) is included in this interval.
2. **For \( -2 < x \leq 2 \), \( f(x) = x + 1 \):**
- This part of the function is a linear function with a slope of 1 and a y-intercept at \((0, 1)\).
- Draw a line starting just to the right of \( x = -2 \), which would begin at approximately \( (-2, -1+1 = -1) \).
- This line continues up to \( x = 2 \) and ends at \( y = 3 \) with a closed dot at \( (2, 3) \).
3. **For \( x > 2 \), \( f(x) = 0 \):**
- This part of the function is a constant value of 0 for all \( x \) values greater than 2.
- Draw a horizontal line at \( y = 0 \) starting from right after \( x = 2 \) towards the right end of the graph.
- Include an open dot at \( (2, 0) \) since \( x = 2 \) is not included in this interval.
## Graph Axes and Scale:
- The x-axis ranges from -5 to 5.
- The y-axis ranges from -5 to 5.
- The graph is drawn on a
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