Write the domain and range of the function using interval notation. Domain: Range: 0 Σ y 1 --2- Show your work and explain how you arrived at your answers. + 2 O 3 4 5 Submit Assignment X R TICV w Quit & Save Back O Ques Nov
Write the domain and range of the function using interval notation. Domain: Range: 0 Σ y 1 --2- Show your work and explain how you arrived at your answers. + 2 O 3 4 5 Submit Assignment X R TICV w Quit & Save Back O Ques Nov
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Title: Understanding Domain and Range Using Interval Notation**
**Introduction:**
In this exercise, we explore how to determine and express the domain and range of a function using interval notation. Understanding these concepts is fundamental in analyzing the behavior of functions.
**Task Description:**
- **Objective:** Write the domain and range of the function using interval notation.
**Graph Analysis:**
The graph provided shows a parabolic function. Here’s a detailed explanation of the graph:
- **Axes:** The graph features a standard Cartesian coordinate system with the x-axis and y-axis both ranging from -5 to 5.
- **Curve:** The function is a downward-opening parabola.
- The left end of the parabola slightly touches the y-axis at approximately y = 3.
- The right end of the parabola is open and heads towards x = 3.
**Determining Domain and Range:**
- **Domain:** The set of all possible x-values that the function can take.
- For this graph, the x-values range from -3 to 3, inclusive of -3 and exclusive of 3.
- **Interval Notation:** \([-3, 3)\)
- **Range:** The set of all possible y-values that the function can output.
- The highest point of the parabola is at y = 3, and it opens downward without extending below y = 1.
- **Interval Notation:** \([1, 3]\)
**Instructions:**
- **Domain:** Enter \([-3, 3)\)
- **Range:** Enter \([1, 3]\)
**Conclusion:**
Understanding how to find and express the domain and range using interval notation helps clarify the input and output limits of functions, a crucial skill in mathematical analysis.
**Note:**
Ensure to show your work and explain how you arrived at your answers for a comprehensive understanding.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f332ee6-3ef6-4e55-bad3-1cebde5ee541%2F9d3db7e8-9cbd-429f-94c2-1e11d1b279ab%2Fx66m44_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Domain and Range Using Interval Notation**
**Introduction:**
In this exercise, we explore how to determine and express the domain and range of a function using interval notation. Understanding these concepts is fundamental in analyzing the behavior of functions.
**Task Description:**
- **Objective:** Write the domain and range of the function using interval notation.
**Graph Analysis:**
The graph provided shows a parabolic function. Here’s a detailed explanation of the graph:
- **Axes:** The graph features a standard Cartesian coordinate system with the x-axis and y-axis both ranging from -5 to 5.
- **Curve:** The function is a downward-opening parabola.
- The left end of the parabola slightly touches the y-axis at approximately y = 3.
- The right end of the parabola is open and heads towards x = 3.
**Determining Domain and Range:**
- **Domain:** The set of all possible x-values that the function can take.
- For this graph, the x-values range from -3 to 3, inclusive of -3 and exclusive of 3.
- **Interval Notation:** \([-3, 3)\)
- **Range:** The set of all possible y-values that the function can output.
- The highest point of the parabola is at y = 3, and it opens downward without extending below y = 1.
- **Interval Notation:** \([1, 3]\)
**Instructions:**
- **Domain:** Enter \([-3, 3)\)
- **Range:** Enter \([1, 3]\)
**Conclusion:**
Understanding how to find and express the domain and range using interval notation helps clarify the input and output limits of functions, a crucial skill in mathematical analysis.
**Note:**
Ensure to show your work and explain how you arrived at your answers for a comprehensive understanding.
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