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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![**Transcription and Explanation for Educational Website**
### Task Instruction
For No. 24, use set-builder notation to state the domain and range.
### Diagram Description
The diagram depicts a graph with two intersecting lines that form an "X" shape with arrows at the ends, indicating that they extend infinitely in both directions. Each line appears to be straight, suggesting linear relationships.
#### Analysis of the Graph:
- There are two lines crossing at the origin.
- One line appears to be a vertical line and the other is a horizontal line, forming the axes of the coordinate plane.
### Explanation:
**Lines:**
1. **Vertical Line:** Extends infinitely in the up and down directions.
2. **Horizontal Line:** Extends infinitely to the left and right.
**Domain and Range:**
Since the lines represent the entire x-axis and y-axis, the domain and range for both lines can be described using set-builder notation.
- **Domain:** The set of all x-values that the graph encompasses.
- For the lines shown (the x-axis and y-axis), the domain can be written as:
\[
\text{Domain: } \{ x \,|\, x \in \mathbb{R} \}
\]
- **Range:** The set of all y-values that the graph includes.
- For the same set of intersecting lines, it is:
\[
\text{Range: } \{ y \,|\, y \in \mathbb{R} \}
\]
**Conclusion:**
This graph effectively illustrates that both lines extend indefinitely, covering all real numbers on both axes, which is expressed in the domain and range using set-builder notation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b0cb7f7-af45-4075-9960-1abbb1a97741%2F0eb1689a-293d-47a1-9daa-5ca909a98104%2Fkvn7rz8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription and Explanation for Educational Website**
### Task Instruction
For No. 24, use set-builder notation to state the domain and range.
### Diagram Description
The diagram depicts a graph with two intersecting lines that form an "X" shape with arrows at the ends, indicating that they extend infinitely in both directions. Each line appears to be straight, suggesting linear relationships.
#### Analysis of the Graph:
- There are two lines crossing at the origin.
- One line appears to be a vertical line and the other is a horizontal line, forming the axes of the coordinate plane.
### Explanation:
**Lines:**
1. **Vertical Line:** Extends infinitely in the up and down directions.
2. **Horizontal Line:** Extends infinitely to the left and right.
**Domain and Range:**
Since the lines represent the entire x-axis and y-axis, the domain and range for both lines can be described using set-builder notation.
- **Domain:** The set of all x-values that the graph encompasses.
- For the lines shown (the x-axis and y-axis), the domain can be written as:
\[
\text{Domain: } \{ x \,|\, x \in \mathbb{R} \}
\]
- **Range:** The set of all y-values that the graph includes.
- For the same set of intersecting lines, it is:
\[
\text{Range: } \{ y \,|\, y \in \mathbb{R} \}
\]
**Conclusion:**
This graph effectively illustrates that both lines extend indefinitely, covering all real numbers on both axes, which is expressed in the domain and range using set-builder notation.
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