Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Determining the Domain and Range of a Function
#### Graph Analysis:
In this graph, several blue points are plotted on a coordinate plane to represent specific values of a function. The x-axis and y-axis range from -5 to 5 in their respective directions.
#### Points on the Graph:
- `(-3, -4)`
- `(-3, 4)`
- `(-1, 3)`
- `(0, 0)`
- `(2, 2)`
- `(2, -1)`
#### Domain and Range:
- **Domain:** The domain of a function represents all the possible \( x \)-values. From the graph, these are the \( x \)-coordinates of all the plotted points.
**Domain:** \(-3, -1, 0, 2\)
- **Range:** The range of a function represents all the possible \( y \)-values. From the graph, these are the \( y \)-coordinates of all the plotted points.
**Range:** \(-4, -1, 0, 2, 3, 4\)
#### Observations:
- The function has distinct values at six different points.
- It is important to note that the same \( x \)-value can have multiple \( y \)-values, as seen from the points \((-3, -4)\) and \((-3, 4)\) or \((2, 2)\) and \((2, -1)\).
This analysis helps in understanding how the function behaves across different input values and the set of outputs it produces.
#### Part 1 of 2
*Please refer to the subsequent parts for more detailed explanations and applications.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73e6f914-049c-4b71-aae0-005ff11f5f5d%2Ffb0673d8-5b06-480a-b992-c9f18b6c88be%2Fepy4m89_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the Domain and Range of a Function
#### Graph Analysis:
In this graph, several blue points are plotted on a coordinate plane to represent specific values of a function. The x-axis and y-axis range from -5 to 5 in their respective directions.
#### Points on the Graph:
- `(-3, -4)`
- `(-3, 4)`
- `(-1, 3)`
- `(0, 0)`
- `(2, 2)`
- `(2, -1)`
#### Domain and Range:
- **Domain:** The domain of a function represents all the possible \( x \)-values. From the graph, these are the \( x \)-coordinates of all the plotted points.
**Domain:** \(-3, -1, 0, 2\)
- **Range:** The range of a function represents all the possible \( y \)-values. From the graph, these are the \( y \)-coordinates of all the plotted points.
**Range:** \(-4, -1, 0, 2, 3, 4\)
#### Observations:
- The function has distinct values at six different points.
- It is important to note that the same \( x \)-value can have multiple \( y \)-values, as seen from the points \((-3, -4)\) and \((-3, 4)\) or \((2, 2)\) and \((2, -1)\).
This analysis helps in understanding how the function behaves across different input values and the set of outputs it produces.
#### Part 1 of 2
*Please refer to the subsequent parts for more detailed explanations and applications.*
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