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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Question
For each graph below, state whether it represents a function.
- **Description**: A graph depicting a diamond shape with its diagonal axis aligned. The graph is centered at the origin (0, 0) and extends symmetrically along both x and y axes.
- **Function?**:
- Yes ☐
- No ☑
#### Graph 2
- **Description**: A collection of multiple blue dots distributed unevenly across the coordinate plane. Some dots share the same x-coordinate but have different y-coordinates.
- **Function?**:
- Yes ☐
- No ☑
#### Graph 3
- **Description**: A scatter plot with dots scattered around the coordinate plane. Several dots are vertically aligned (same x-coordinates).
- **Function?**:
- Yes ☐
- No ☑
#### Graph 4
- **Description**: A piecewise linear graph composed of two line segments meeting at a point. One segment is inclined upwards at a constant rate, and the other is inclined downwards.
- **Function?**:
- Yes ☑
- No ☐
#### Graph 5
- **Description**: A graph representing a parabola opening upwards with its vertex at the origin.
- **Function?**:
- Yes ☑
- No ☐
#### Graph 6
- **Description**: A graph composed of individual points connected by line segments. Some points are vertically aligned (same x-coordinates).
- **Function?**:
- Yes ☐
- No ☑
### Explanation
Graphs that represent functions must pass the **Vertical Line Test**. This test states that if a vertical line intersects a graph at more than one point, then the graph does not represent a function. In our examples:
- Graphs 1, 2, 3, and 6 do not pass the vertical line test (vertical lines intersect the graph at more than one point).
- Graphs 4 and 5 pass the vertical line test (](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64f54e3f-bbb2-46db-a1a9-bb995302d054%2Fb07f1f17-20e9-4f6c-ac3b-fcfe4115fc00%2Frk18nnp.png&w=3840&q=75)
Transcribed Image Text:### Identifying Functions from Graphs
For each graph below, state whether it represents a function.
#### Graph 1
- **Description**: A graph depicting a diamond shape with its diagonal axis aligned. The graph is centered at the origin (0, 0) and extends symmetrically along both x and y axes.
- **Function?**:
- Yes ☐
- No ☑
#### Graph 2
- **Description**: A collection of multiple blue dots distributed unevenly across the coordinate plane. Some dots share the same x-coordinate but have different y-coordinates.
- **Function?**:
- Yes ☐
- No ☑
#### Graph 3
- **Description**: A scatter plot with dots scattered around the coordinate plane. Several dots are vertically aligned (same x-coordinates).
- **Function?**:
- Yes ☐
- No ☑
#### Graph 4
- **Description**: A piecewise linear graph composed of two line segments meeting at a point. One segment is inclined upwards at a constant rate, and the other is inclined downwards.
- **Function?**:
- Yes ☑
- No ☐
#### Graph 5
- **Description**: A graph representing a parabola opening upwards with its vertex at the origin.
- **Function?**:
- Yes ☑
- No ☐
#### Graph 6
- **Description**: A graph composed of individual points connected by line segments. Some points are vertically aligned (same x-coordinates).
- **Function?**:
- Yes ☐
- No ☑
### Explanation
Graphs that represent functions must pass the **Vertical Line Test**. This test states that if a vertical line intersects a graph at more than one point, then the graph does not represent a function. In our examples:
- Graphs 1, 2, 3, and 6 do not pass the vertical line test (vertical lines intersect the graph at more than one point).
- Graphs 4 and 5 pass the vertical line test (
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