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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![### Finding the Domain and Range of a Relation from the Graph
To determine the domain and range of the relation shown in the graph provided, follow these steps:
1. **Domain**: The domain of a relation is the set of all possible input values (x-values). To find the domain, identify the minimum and maximum x-values on the graph.
2. **Range**: The range of a relation is the set of all possible output values (y-values). To find the range, identify the minimum and maximum y-values on the graph.
#### Analysis of the Graph:
- The graph is a piecewise linear relation drawn on a coordinate plane with the x-axis ranging from -10 to 10 and the y-axis ranging from -10 to 10.
- The relation consists of three line segments. Each segment is represented by arrows pointing in the direction of the relation:
1. The first segment starts at point (-10, 0) and moves upwards to point (0, 10).
2. The second segment is a horizontal line extending from point (0, 10) to point (5, 10).
3. The third segment descends from point (5, 10) to point (10, 0).
#### Domain:
- The x-values of the relation extend from -10 to 10.
- Therefore, the domain of the relation is:
\[
\text{Domain} = \left\{ x \, | \, -10 \leq x \leq 10 \right\}
\]
#### Range:
- The y-values of the relation extend from 0 to 10.
- Therefore, the range of the relation is:
\[
\text{Range} = \left\{ y \, | \, 0 \leq y \leq 10 \right\}
\]
### Summary:
The domain and range of the given relation are derived from the graphed line segments and tell us the span of x-values and y-values that the relation covers. Here:
- The domain is \(-10 \leq x \leq 10\).
- The range is \(0 \leq y \leq 10\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F248ffd31-6bd8-4a0d-a8ec-50177a1e4ef9%2F8526995c-ea9e-40f1-b11e-03565f8798d4%2Flnfqu1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Domain and Range of a Relation from the Graph
To determine the domain and range of the relation shown in the graph provided, follow these steps:
1. **Domain**: The domain of a relation is the set of all possible input values (x-values). To find the domain, identify the minimum and maximum x-values on the graph.
2. **Range**: The range of a relation is the set of all possible output values (y-values). To find the range, identify the minimum and maximum y-values on the graph.
#### Analysis of the Graph:
- The graph is a piecewise linear relation drawn on a coordinate plane with the x-axis ranging from -10 to 10 and the y-axis ranging from -10 to 10.
- The relation consists of three line segments. Each segment is represented by arrows pointing in the direction of the relation:
1. The first segment starts at point (-10, 0) and moves upwards to point (0, 10).
2. The second segment is a horizontal line extending from point (0, 10) to point (5, 10).
3. The third segment descends from point (5, 10) to point (10, 0).
#### Domain:
- The x-values of the relation extend from -10 to 10.
- Therefore, the domain of the relation is:
\[
\text{Domain} = \left\{ x \, | \, -10 \leq x \leq 10 \right\}
\]
#### Range:
- The y-values of the relation extend from 0 to 10.
- Therefore, the range of the relation is:
\[
\text{Range} = \left\{ y \, | \, 0 \leq y \leq 10 \right\}
\]
### Summary:
The domain and range of the given relation are derived from the graphed line segments and tell us the span of x-values and y-values that the relation covers. Here:
- The domain is \(-10 \leq x \leq 10\).
- The range is \(0 \leq y \leq 10\).
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