Sketch a graph of f(x) = 87 Clear All Draw: 7 65432 -5 1 -8-7-6-5 -4 -3 -2 -1 -1 12345678 -2 -4 -5 -6 -7 -8+ -3x+4 if I < 2 -2x+1 if I > 2 1 2 3 4 5 6 7 8 //n O
Sketch a graph of f(x) = 87 Clear All Draw: 7 65432 -5 1 -8-7-6-5 -4 -3 -2 -1 -1 12345678 -2 -4 -5 -6 -7 -8+ -3x+4 if I < 2 -2x+1 if I > 2 1 2 3 4 5 6 7 8 //n O
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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![## Sketching a Piecewise Function
### Problem Statement
Sketch a graph of the piecewise function \( f(x) \) defined as:
\[ f(x) = \begin{cases}
-3x + 4 & \text{if } x < 2 \\
-2x + 1 & \text{if } x \geq 2
\end{cases} \]
### Instructions
1. **Understanding the Function:**
- **For \( x < 2 \):** Use the linear function \( -3x + 4 \).
- **For \( x \geq 2 \):** Use the linear function \( -2x + 1 \).
2. **Graph Paper:**
- The provided graph is a standard Cartesian plane with the x-axis and y-axis labeled from -8 to 8.
3. **Plotting the Function:**
- For \( x < 2 \):
- The equation is \( -3x + 4 \).
- This is a straight line with a slope of -3 and a y-intercept at 4.
- For \( x \geq 2 \):
- The equation is \( -2x + 1 \).
- This is a straight line with a slope of -2 and a y-intercept at 1.
4. **Special Points:**
- For \( x = 2 \):
- Calculate \( f(2) \) for both pieces.
- For \( -3x + 4 \), when \( x = 2 \), \( y = -3(2) + 4 = -6 + 4 = -2 \).
- For \( -2x + 1 \), when \( x = 2 \), \( y = -2(2) + 1 = -4 + 1 = -3 \).
### Graph Construction
- **Graph of \( -3x + 4 \) for \( x < 2 \):**
- The line will have an open circle at \( (2, -2) \) and continue for all \( x < 2 \).
- Plot a few points to help draw this line, such as:
- When \( x = 0 \), \( y = 4 \).
- When \( x = 1 \), \( y =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab90fdf9-da41-461c-9056-08da6acfe393%2F926b2c15-5107-4287-9be8-873624b7e8b8%2Fwr3cymd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Sketching a Piecewise Function
### Problem Statement
Sketch a graph of the piecewise function \( f(x) \) defined as:
\[ f(x) = \begin{cases}
-3x + 4 & \text{if } x < 2 \\
-2x + 1 & \text{if } x \geq 2
\end{cases} \]
### Instructions
1. **Understanding the Function:**
- **For \( x < 2 \):** Use the linear function \( -3x + 4 \).
- **For \( x \geq 2 \):** Use the linear function \( -2x + 1 \).
2. **Graph Paper:**
- The provided graph is a standard Cartesian plane with the x-axis and y-axis labeled from -8 to 8.
3. **Plotting the Function:**
- For \( x < 2 \):
- The equation is \( -3x + 4 \).
- This is a straight line with a slope of -3 and a y-intercept at 4.
- For \( x \geq 2 \):
- The equation is \( -2x + 1 \).
- This is a straight line with a slope of -2 and a y-intercept at 1.
4. **Special Points:**
- For \( x = 2 \):
- Calculate \( f(2) \) for both pieces.
- For \( -3x + 4 \), when \( x = 2 \), \( y = -3(2) + 4 = -6 + 4 = -2 \).
- For \( -2x + 1 \), when \( x = 2 \), \( y = -2(2) + 1 = -4 + 1 = -3 \).
### Graph Construction
- **Graph of \( -3x + 4 \) for \( x < 2 \):**
- The line will have an open circle at \( (2, -2) \) and continue for all \( x < 2 \).
- Plot a few points to help draw this line, such as:
- When \( x = 0 \), \( y = 4 \).
- When \( x = 1 \), \( y =
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