**Graphs and Functions** **Domain and Range from the Graph of a Continuous Function** The entire graph of the function \( g \) is shown in the figure below. Write the domain and range of \( g \) using interval notation. **Graph Explanation:** The graph depicts a continuous function with the following characteristics: - The function starts at the point \((-2, 0)\) and ends at the point \( (3, -4)\). - It is a smooth curve that reaches a maximum point at approximately \( (0, 4) \). - The endpoints \((-2, 0)\) and \( (3, -4)\) are open circles, indicating that these points are not included in the function. **Domain and Range:** (a) **Domain:** The interval where the function exists along the x-axis. (b) **Range:** The interval representing the possible output values (y-values). **Options for Interval Notation:** The options provided for selecting the domain and range are various forms of intervals and symbols: - \(( , )\) (open interval) - \([ , ]\) (closed interval) - Combination of open and closed intervals - Union symbol (\( \cup \)) - Empty set symbol (\( \emptyset \)) - Infinity symbols (\(\infty, -\infty\)) You need to choose the appropriate intervals to correctly represent the domain and range of the function \( g \).
**Graphs and Functions** **Domain and Range from the Graph of a Continuous Function** The entire graph of the function \( g \) is shown in the figure below. Write the domain and range of \( g \) using interval notation. **Graph Explanation:** The graph depicts a continuous function with the following characteristics: - The function starts at the point \((-2, 0)\) and ends at the point \( (3, -4)\). - It is a smooth curve that reaches a maximum point at approximately \( (0, 4) \). - The endpoints \((-2, 0)\) and \( (3, -4)\) are open circles, indicating that these points are not included in the function. **Domain and Range:** (a) **Domain:** The interval where the function exists along the x-axis. (b) **Range:** The interval representing the possible output values (y-values). **Options for Interval Notation:** The options provided for selecting the domain and range are various forms of intervals and symbols: - \(( , )\) (open interval) - \([ , ]\) (closed interval) - Combination of open and closed intervals - Union symbol (\( \cup \)) - Empty set symbol (\( \emptyset \)) - Infinity symbols (\(\infty, -\infty\)) You need to choose the appropriate intervals to correctly represent the domain and range of the function \( g \).
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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![**Graphs and Functions**
**Domain and Range from the Graph of a Continuous Function**
The entire graph of the function \( g \) is shown in the figure below. Write the domain and range of \( g \) using interval notation.
**Graph Explanation:**
The graph depicts a continuous function with the following characteristics:
- The function starts at the point \((-2, 0)\) and ends at the point \( (3, -4)\).
- It is a smooth curve that reaches a maximum point at approximately \( (0, 4) \).
- The endpoints \((-2, 0)\) and \( (3, -4)\) are open circles, indicating that these points are not included in the function.
**Domain and Range:**
(a) **Domain:** The interval where the function exists along the x-axis.
(b) **Range:** The interval representing the possible output values (y-values).
**Options for Interval Notation:**
The options provided for selecting the domain and range are various forms of intervals and symbols:
- \(( , )\) (open interval)
- \([ , ]\) (closed interval)
- Combination of open and closed intervals
- Union symbol (\( \cup \))
- Empty set symbol (\( \emptyset \))
- Infinity symbols (\(\infty, -\infty\))
You need to choose the appropriate intervals to correctly represent the domain and range of the function \( g \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F299ab521-a5b0-47a9-a17f-05b75826b9b4%2F5df45976-5500-41de-aca3-74a70ecd9e55%2Fmog6mn.jpeg&w=3840&q=75)
Transcribed Image Text:**Graphs and Functions**
**Domain and Range from the Graph of a Continuous Function**
The entire graph of the function \( g \) is shown in the figure below. Write the domain and range of \( g \) using interval notation.
**Graph Explanation:**
The graph depicts a continuous function with the following characteristics:
- The function starts at the point \((-2, 0)\) and ends at the point \( (3, -4)\).
- It is a smooth curve that reaches a maximum point at approximately \( (0, 4) \).
- The endpoints \((-2, 0)\) and \( (3, -4)\) are open circles, indicating that these points are not included in the function.
**Domain and Range:**
(a) **Domain:** The interval where the function exists along the x-axis.
(b) **Range:** The interval representing the possible output values (y-values).
**Options for Interval Notation:**
The options provided for selecting the domain and range are various forms of intervals and symbols:
- \(( , )\) (open interval)
- \([ , ]\) (closed interval)
- Combination of open and closed intervals
- Union symbol (\( \cup \))
- Empty set symbol (\( \emptyset \))
- Infinity symbols (\(\infty, -\infty\))
You need to choose the appropriate intervals to correctly represent the domain and range of the function \( g \).
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