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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Question
![The image presents a piecewise function defined as follows:
\[ f(x) =
\begin{cases}
4x + 12 & \text{for } x \leq -2 \\
-2x + 6 & \text{for } -1 \leq x
\end{cases} \]
A graph accompanies this function, plotted on a coordinate plane with the x-axis ranging from -3 to 3 and the y-axis ranging from 0 to 10. The graph consists of two linear segments:
1. **First segment (green line)**: This line represents the function \(4x + 12\) and is drawn for \(x \leq -2\). The graph of this line is decreasing as it moves leftwards from the y-intercept at (0, 12).
2. **Second segment (red line)**: This line represents the function \(-2x + 6\) and is drawn for \(-1 \leq x\). The graph of this line descends toward the x-axis.
**Features of the Graph:**
- The piecewise function transitions at \(x = -2\) and \(x = -1\).
- The lines intersect at a peak at approximately \((0, 6)\).
**Questions:**
- **What is the relative maximum?**
- **What is the relative minimum?**
**Evaluations:**
21. Evaluate the function for \(f(-2)=\)
22. Evaluate the function for \(f(1)=\)
These elements provide a comprehensive understanding of the piecewise function and allow for practical evaluation opportunities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd448e554-bc82-421e-b90e-d21b0f402f1e%2F45fbc61d-925b-4784-ba4a-35bccfc234de%2Fzy3w1qr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image presents a piecewise function defined as follows:
\[ f(x) =
\begin{cases}
4x + 12 & \text{for } x \leq -2 \\
-2x + 6 & \text{for } -1 \leq x
\end{cases} \]
A graph accompanies this function, plotted on a coordinate plane with the x-axis ranging from -3 to 3 and the y-axis ranging from 0 to 10. The graph consists of two linear segments:
1. **First segment (green line)**: This line represents the function \(4x + 12\) and is drawn for \(x \leq -2\). The graph of this line is decreasing as it moves leftwards from the y-intercept at (0, 12).
2. **Second segment (red line)**: This line represents the function \(-2x + 6\) and is drawn for \(-1 \leq x\). The graph of this line descends toward the x-axis.
**Features of the Graph:**
- The piecewise function transitions at \(x = -2\) and \(x = -1\).
- The lines intersect at a peak at approximately \((0, 6)\).
**Questions:**
- **What is the relative maximum?**
- **What is the relative minimum?**
**Evaluations:**
21. Evaluate the function for \(f(-2)=\)
22. Evaluate the function for \(f(1)=\)
These elements provide a comprehensive understanding of the piecewise function and allow for practical evaluation opportunities.
Expert Solution
Step 1
We first sketch the function
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