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.

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### 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.
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