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 Domain and Range in Graphing Functions
**Graph Analysis**
The graph provided is of a particular function that shows the relationship between \(x\) (independent variable) and \(y\) (dependent variable). This function is graphed on a coordinate system with \(x\)-axis ranging from -5 to 5 and \(y\)-axis ranging from -5 to 5.
- The graph starts at point \((-2, 0)\) which is indicated by a solid blue dot, implying this point is included in the function.
- The graph curves upwards, reaching a maximum point at \((0, 4)\).
- It then curves downward, and the graph ends at the point \((2, -5)\), indicated by an open circle, which means this value is not included in the function.
**Domain and Range**
- **Domain:** This is the set of all possible \(x\)-values (inputs) for which the function is defined. For the given graph, the function starts at \(x = -2\) and ends at \(x = 2\). However, based on the open circle, \(x = 2\) is not included. Hence, the domain is \([-2, 0)\).
- **Range:** This is the set of all possible \(y\)-values (outputs) covered by the function. Here, the lowest point on the \(y\)-axis that the function reaches is \(y = -5\) and the highest point is \(y = 4\). Both these values are included, which makes the range \([-5, 4]\).
**Summary Table**
The domain and range of the function are summarized in the table below:
| Domain | Range |
|--------|--------|
| \([-2, 0)\) | \([-5, 4]\)|
This table is a quick reference for understanding the extent of input and output values for the function displayed in the graph. By analyzing these, one can understand the behavior and constraints of the function represented.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa21e1c50-d204-4b1c-af4d-5bfcd54fd78e%2F291829ad-b488-4efd-a5b0-add15b63e869%2Fewwged_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Domain and Range in Graphing Functions
**Graph Analysis**
The graph provided is of a particular function that shows the relationship between \(x\) (independent variable) and \(y\) (dependent variable). This function is graphed on a coordinate system with \(x\)-axis ranging from -5 to 5 and \(y\)-axis ranging from -5 to 5.
- The graph starts at point \((-2, 0)\) which is indicated by a solid blue dot, implying this point is included in the function.
- The graph curves upwards, reaching a maximum point at \((0, 4)\).
- It then curves downward, and the graph ends at the point \((2, -5)\), indicated by an open circle, which means this value is not included in the function.
**Domain and Range**
- **Domain:** This is the set of all possible \(x\)-values (inputs) for which the function is defined. For the given graph, the function starts at \(x = -2\) and ends at \(x = 2\). However, based on the open circle, \(x = 2\) is not included. Hence, the domain is \([-2, 0)\).
- **Range:** This is the set of all possible \(y\)-values (outputs) covered by the function. Here, the lowest point on the \(y\)-axis that the function reaches is \(y = -5\) and the highest point is \(y = 4\). Both these values are included, which makes the range \([-5, 4]\).
**Summary Table**
The domain and range of the function are summarized in the table below:
| Domain | Range |
|--------|--------|
| \([-2, 0)\) | \([-5, 4]\)|
This table is a quick reference for understanding the extent of input and output values for the function displayed in the graph. By analyzing these, one can understand the behavior and constraints of the function represented.
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