The graph of a piecewise-defined function is given. Write a definition for the function that best describes this graph. (3.3) -7 if xs f(x) = if 0
The graph of a piecewise-defined function is given. Write a definition for the function that best describes this graph. (3.3) -7 if xs f(x) = if 0
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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![The task is to write a definition for a piecewise-defined function that accurately describes the provided graph.
### Explanation of the Graph:
- The graph consists of two linear segments.
- **Segment 1**: Starts from point \((-3, 3)\) and moves to \( (0, 0) \). This segment has a closed circle at \((-3, 3)\) and an open circle at \( (0, 0) \), indicating that the segment includes \(-3\) but not \(0\).
- **Segment 2**: Starts from point \( (0, 0) \) and moves to \((3, 2)\). This segment has an open circle at \( (0, 0) \) and a closed circle at \( (3, 2) \), indicating that the segment includes \(3\) but not \(0\).
### Piecewise Function Definition:
The function \( f(x) \) is defined as follows:
- \( f(x) \) has two expressions corresponding to each of the segments explained.
1. For the first segment:
\[
f(x) = mx + b_1 \quad \text{if} \quad x \leq 0
\]
2. For the second segment:
\[
f(x) = mx + b_2 \quad \text{if} \quad 0 < x \leq 3
\]
These expressions need to be calculated based on the slopes and intercepts of the lines in the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff32868be-10a6-45e0-938e-9e0ea4b8c441%2Fa7391c5e-c5cf-4e49-8045-371aa4fc6821%2Fq3ww9cf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The task is to write a definition for a piecewise-defined function that accurately describes the provided graph.
### Explanation of the Graph:
- The graph consists of two linear segments.
- **Segment 1**: Starts from point \((-3, 3)\) and moves to \( (0, 0) \). This segment has a closed circle at \((-3, 3)\) and an open circle at \( (0, 0) \), indicating that the segment includes \(-3\) but not \(0\).
- **Segment 2**: Starts from point \( (0, 0) \) and moves to \((3, 2)\). This segment has an open circle at \( (0, 0) \) and a closed circle at \( (3, 2) \), indicating that the segment includes \(3\) but not \(0\).
### Piecewise Function Definition:
The function \( f(x) \) is defined as follows:
- \( f(x) \) has two expressions corresponding to each of the segments explained.
1. For the first segment:
\[
f(x) = mx + b_1 \quad \text{if} \quad x \leq 0
\]
2. For the second segment:
\[
f(x) = mx + b_2 \quad \text{if} \quad 0 < x \leq 3
\]
These expressions need to be calculated based on the slopes and intercepts of the lines in the graph.
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