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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![### DO NOW: Determine if each graph represents a function.
#### Graph Descriptions:
##### Graph 1:
The first graph consists of a series of discrete points. These points appear to form a somewhat vertical pattern, increasing from left to right. Each x-value corresponds to exactly one y-value, indicating that this graph represents a function. Specifically:
- On the left, the points are closer together and become more spaced out as we move to the right.
##### Graph 2:
The second graph shows two lines forming a 'V' shape, converging at the origin (0,0). Both lines extend indefinitely. This graph does not represent a function, as there are multiple y-values for a single x-value for all x ≠ 0. Specifically:
- Both arms of the 'V' intersect the y-axis at different points, violating the vertical line test.
##### Graph 3:
The third graph displays a single straight line that passes through the origin and extends in both directions. This graph represents a function, as each x-value has a unique y-value, satisfying the vertical line test. Specifically:
- The line slopes upward from left to right, indicating a positive relationship between x and y values.
### Summary:
1. **First Graph**: Represents a function (discrete points with unique y-values for each x).
2. **Second Graph**: Does not represent a function (‘V’ shape with multiple y-values for single x-values).
3. **Third Graph**: Represents a function (continuous line passing through the origin with unique y-values for each x-value).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53fa1db3-32f8-4c94-8cb8-72dc1b15d364%2F0fa79514-7dc2-4cce-a59b-835356f4eb4b%2Fvveqbm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### DO NOW: Determine if each graph represents a function.
#### Graph Descriptions:
##### Graph 1:
The first graph consists of a series of discrete points. These points appear to form a somewhat vertical pattern, increasing from left to right. Each x-value corresponds to exactly one y-value, indicating that this graph represents a function. Specifically:
- On the left, the points are closer together and become more spaced out as we move to the right.
##### Graph 2:
The second graph shows two lines forming a 'V' shape, converging at the origin (0,0). Both lines extend indefinitely. This graph does not represent a function, as there are multiple y-values for a single x-value for all x ≠ 0. Specifically:
- Both arms of the 'V' intersect the y-axis at different points, violating the vertical line test.
##### Graph 3:
The third graph displays a single straight line that passes through the origin and extends in both directions. This graph represents a function, as each x-value has a unique y-value, satisfying the vertical line test. Specifically:
- The line slopes upward from left to right, indicating a positive relationship between x and y values.
### Summary:
1. **First Graph**: Represents a function (discrete points with unique y-values for each x).
2. **Second Graph**: Does not represent a function (‘V’ shape with multiple y-values for single x-values).
3. **Third Graph**: Represents a function (continuous line passing through the origin with unique y-values for each x-value).
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