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
![**Determining the Domain of a Linear Function**
In this exercise, we are tasked with finding the domain of the given function and expressing it using interval notation. The provided graph illustrates a linear function represented by a line segment.
1. **Graph Details**:
- The x-axis extends horizontally from -6 to 6.
- The y-axis extends vertically from -6 to 6.
- The line segment starts at the point (-1, 4) and ends at the point (6, 0).
2. **Line Segment Analysis**:
- The function is valid for all x-values that fall between -1 and 6, including both endpoints, because the line segment includes both initial and terminal points.
3. **Interpretation**:
- The domain of the function is the set of all x-values for which the function is defined.
- In this case, the function is defined from x = -1 to x = 6.
4. **Writing Domain in Interval Notation**:
- Interval notation concisely denotes the domain as [-1, 6].
- The square brackets [ ] indicate that the endpoints -1 and 6 are included in the domain.
Therefore, the domain of this function, written in interval notation, is:
\[ \text{The domain is: } [-1, 6] \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab90fdf9-da41-461c-9056-08da6acfe393%2Fd0a188e6-8f71-4d84-aac5-c69aa2b2aa48%2Ftnx5snw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determining the Domain of a Linear Function**
In this exercise, we are tasked with finding the domain of the given function and expressing it using interval notation. The provided graph illustrates a linear function represented by a line segment.
1. **Graph Details**:
- The x-axis extends horizontally from -6 to 6.
- The y-axis extends vertically from -6 to 6.
- The line segment starts at the point (-1, 4) and ends at the point (6, 0).
2. **Line Segment Analysis**:
- The function is valid for all x-values that fall between -1 and 6, including both endpoints, because the line segment includes both initial and terminal points.
3. **Interpretation**:
- The domain of the function is the set of all x-values for which the function is defined.
- In this case, the function is defined from x = -1 to x = 6.
4. **Writing Domain in Interval Notation**:
- Interval notation concisely denotes the domain as [-1, 6].
- The square brackets [ ] indicate that the endpoints -1 and 6 are included in the domain.
Therefore, the domain of this function, written in interval notation, is:
\[ \text{The domain is: } [-1, 6] \]
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