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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![### Understanding the Domain of the Graphed Function
The problem "Find the domain of the function graphed" requires an analysis of the graph shown. The graph features a Cartesian coordinate plane with an x-axis ranging from -8 to 8 and a y-axis ranging from -8 to 8.
#### Graph Description:
1. **Horizontal Lines:**
- There is a solid horizontal line extending from \( x = -8 \) to \( x = -2 \), passing through \( y = -2 \).
- Another solid horizontal line extends from \( x = 2 \) to the right, passing through \( y = 2 \).
2. **Open Circles:**
- An open circle is located at the point \( (2, 2) \).
- Another open circle is located at the point \( (-2, -2) \).
#### Domain Explanation:
The domain of a function consists of all the possible x-values for which the function is defined. Based on the graph:
- The function is defined from \( x = -8 \) to \( x = -2 \) on the line passing through \( y = -2 \). This line is continuous and solid, indicating that all these x-values are included.
- The function is undefined precisely at \( x = -2 \) due to the open circle at \( (-2, -2) \).
- The function is undefined from \( x = -2 \) to \( x = 2 \).
- The function is defined from \( x = 2 \) to the right on the line passing through \( y = 2 \), and this line is continuous and solid, indicating all these x-values are included as well.
- The function is undefined precisely at \( x = 2 \) due to the open circle at \( (2, 2) \).
Thus, combining all the segments, the domain of the function is:
\[ \text{Domain} = (-8, -2) \cup (2, \infty) \]
This can be read as:
- The function includes all x-values from -8 to -2 (not including -2).
- The function also includes all x-values greater than 2.
Understanding the domain allows us to know the input values for which the function is defined and can be practically used.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ddf5237-61ec-402c-bcef-2feae18f38a9%2F31dbe03e-9706-410e-bb1e-8dc929db73f5%2Fs70sw2g_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding the Domain of the Graphed Function
The problem "Find the domain of the function graphed" requires an analysis of the graph shown. The graph features a Cartesian coordinate plane with an x-axis ranging from -8 to 8 and a y-axis ranging from -8 to 8.
#### Graph Description:
1. **Horizontal Lines:**
- There is a solid horizontal line extending from \( x = -8 \) to \( x = -2 \), passing through \( y = -2 \).
- Another solid horizontal line extends from \( x = 2 \) to the right, passing through \( y = 2 \).
2. **Open Circles:**
- An open circle is located at the point \( (2, 2) \).
- Another open circle is located at the point \( (-2, -2) \).
#### Domain Explanation:
The domain of a function consists of all the possible x-values for which the function is defined. Based on the graph:
- The function is defined from \( x = -8 \) to \( x = -2 \) on the line passing through \( y = -2 \). This line is continuous and solid, indicating that all these x-values are included.
- The function is undefined precisely at \( x = -2 \) due to the open circle at \( (-2, -2) \).
- The function is undefined from \( x = -2 \) to \( x = 2 \).
- The function is defined from \( x = 2 \) to the right on the line passing through \( y = 2 \), and this line is continuous and solid, indicating all these x-values are included as well.
- The function is undefined precisely at \( x = 2 \) due to the open circle at \( (2, 2) \).
Thus, combining all the segments, the domain of the function is:
\[ \text{Domain} = (-8, -2) \cup (2, \infty) \]
This can be read as:
- The function includes all x-values from -8 to -2 (not including -2).
- The function also includes all x-values greater than 2.
Understanding the domain allows us to know the input values for which the function is defined and can be practically used.
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