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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The graph of a quadratic function with vertex (-2,2) is shown in the figure below. Find the range and domain, and write the range and domain using interval notation
![**Polynomial and Rational Functions**
### Domain and Range from the Graph of a Quadratic Function
**Instructions:**
The graph of a quadratic function with vertex \((-2, 2)\) is shown in the figure below. Find the **range** and the **domain**.
![Graph]()
- **Description:** The graph provided is an upward-opening parabola, denoted in purple.
- **Vertex:** The vertex of the parabola is at \((-2, 2)\).
- **XAxis:** The x-axis ranges from \(-10\) to \(10\).
- **YAxis:** The y-axis ranges from \(-10\) to \(10\).
**Task:**
Write the range and domain using **interval notation**.
**Response Fields:**
- **range =** [ ] _(Input field provided)_
**Buttons:**
- **Explanation**
- **Check**
© 2020 McGraw Hill
**Explanation:**
1. **Domain** refers to the set of all possible x-values that a function can take. For this quadratic function, the parabola extends infinitely to the left and right. Therefore, the domain in interval notation is \((-∞,∞)\).
2. **Range** refers to the set of all possible y-values that a function can take. Since the parabola opens downward with a vertex of \((-2,2)\), the highest point on the graph is \(y = 2\). Therefore, the range in interval notation is \((∞, 2]\).
**Interactive Section:**
- Users are required to input the range using interval notation based on the given quadratic function.
- Clicking "Check" will validate the user's input.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47786e8c-2a51-4f4e-a0fc-479b515f394a%2F32b676a0-cd68-4581-a4b3-f2d838a254ee%2F40zzdf7.jpeg&w=3840&q=75)
Transcribed Image Text:**Polynomial and Rational Functions**
### Domain and Range from the Graph of a Quadratic Function
**Instructions:**
The graph of a quadratic function with vertex \((-2, 2)\) is shown in the figure below. Find the **range** and the **domain**.
![Graph]()
- **Description:** The graph provided is an upward-opening parabola, denoted in purple.
- **Vertex:** The vertex of the parabola is at \((-2, 2)\).
- **XAxis:** The x-axis ranges from \(-10\) to \(10\).
- **YAxis:** The y-axis ranges from \(-10\) to \(10\).
**Task:**
Write the range and domain using **interval notation**.
**Response Fields:**
- **range =** [ ] _(Input field provided)_
**Buttons:**
- **Explanation**
- **Check**
© 2020 McGraw Hill
**Explanation:**
1. **Domain** refers to the set of all possible x-values that a function can take. For this quadratic function, the parabola extends infinitely to the left and right. Therefore, the domain in interval notation is \((-∞,∞)\).
2. **Range** refers to the set of all possible y-values that a function can take. Since the parabola opens downward with a vertex of \((-2,2)\), the highest point on the graph is \(y = 2\). Therefore, the range in interval notation is \((∞, 2]\).
**Interactive Section:**
- Users are required to input the range using interval notation based on the given quadratic function.
- Clicking "Check" will validate the user's input.
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