3. Which graphical representation has a domain of all real numbers? Graph (1) Graph (2) 4 -2 Graph (3) Graph (4) 3 2- 12 34 5X -1- 54 32 -2- -3- 2. 4.

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,...
icon
Related questions
Question
### Educational Content

**Question:**
3. Which graphical representation has a domain of all real numbers?

**Graphs:**

- **Graph (1)**:
  - This graph features a series of discrete points plotted at various coordinates. The points' x and y-coordinates are: 
    - (-3, 2)
    - (-2, -4)
    - (-1, 1)
    - (-1, -2)
    - (0, 0)
    - (1, 2)
    - (2, 3)
    - (3, 1)

- **Graph (2)**:
  - This graph represents a line segment with endpoints. The line passes through the points:
    - (-3, -3)
    - (3, 3)
  - The x-values in this segment are limited to the interval \([-3, 3]\).

- **Graph (3)**:
  - This graph shows an arrow originating from a point and extending to infinity in the positive x-direction. The line appears to start from:
    - (-3, 0)
    - With an arrow pointing indefinitely to the right across the positive x-axis.
  - This indicates that the domain begins from around x = -3 and extends infinitely to the right.

- **Graph (4)**:
  - This graph depicts a diagonal line that extends infinitely in both the positive and negative x-directions.
  - The line passes through:
    - (-2, -2)
    - (2, 2)
  - Continues infinitely in both directions, indicating all real numbers are included in the domain.

### Explanation:
- Domains are the set of all x-values that a function can take.
- **Graph (4)**, representing a line that extends indefinitely in both directions, has a domain of all real numbers \((-\infty, +\infty)\). This means that for any real number x, there is a corresponding y-value on the line.

**Conclusion:** Graph (4) has a domain of all real numbers.
Transcribed Image Text:### Educational Content **Question:** 3. Which graphical representation has a domain of all real numbers? **Graphs:** - **Graph (1)**: - This graph features a series of discrete points plotted at various coordinates. The points' x and y-coordinates are: - (-3, 2) - (-2, -4) - (-1, 1) - (-1, -2) - (0, 0) - (1, 2) - (2, 3) - (3, 1) - **Graph (2)**: - This graph represents a line segment with endpoints. The line passes through the points: - (-3, -3) - (3, 3) - The x-values in this segment are limited to the interval \([-3, 3]\). - **Graph (3)**: - This graph shows an arrow originating from a point and extending to infinity in the positive x-direction. The line appears to start from: - (-3, 0) - With an arrow pointing indefinitely to the right across the positive x-axis. - This indicates that the domain begins from around x = -3 and extends infinitely to the right. - **Graph (4)**: - This graph depicts a diagonal line that extends infinitely in both the positive and negative x-directions. - The line passes through: - (-2, -2) - (2, 2) - Continues infinitely in both directions, indicating all real numbers are included in the domain. ### Explanation: - Domains are the set of all x-values that a function can take. - **Graph (4)**, representing a line that extends indefinitely in both directions, has a domain of all real numbers \((-\infty, +\infty)\). This means that for any real number x, there is a corresponding y-value on the line. **Conclusion:** Graph (4) has a domain of all real numbers.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Parabolas
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education