Math Problem Statement
Are they functions? Analyze the given relations, table of values, graph, and mapping diagram to determine if they represent functions.
Solution
Let’s analyze each case to determine whether they are functions:
5. Relation: {(3, 7), (4, 7), (5, 7), (6, 7)}
- Analysis: In this set of ordered pairs, each input has exactly one output . Specifically:
- Conclusion: This is a function because no -value is repeated with different -values.
6. Table of values:
-7 | -5 | -7 | 5 | |
---|---|---|---|---|
1 | 3 | -1 | 13 |
- Analysis: In this table:
- The is paired with both and . This means that the same input () gives two different outputs.
- Conclusion: This is not a function because an input cannot have more than one output.
7. Graph:
- Analysis: This is a vertical set of arrows, with one arrow per -coordinate pointing to various -values. Using the vertical line test:
- A vertical line passes through more than one point on the graph (e.g., the line at crosses arrows pointing to different -values).
- Conclusion: This is not a function because the vertical line test fails.
8. Graph:
- Analysis: This graph shows a horizontal line at . Using the vertical line test:
- A vertical line intersects the graph at only one point for any -value.
- Conclusion: This is a function because the vertical line test is satisfied.
9. Mapping diagram:
- Analysis: In the diagram:
- maps to both and .
- Conclusion: This is not a function because the same input () has multiple outputs.
Summary of Results:
- 5: Function
- 6: Not a function
- 7: Not a function
- 8: Function
- 9: Not a function
Do you want a more detailed explanation or have questions?
Here are 5 related questions to deepen your understanding:
- What is the formal definition of a function?
- How can you apply the vertical line test to any graph?
- Why does having one -value map to multiple -values disqualify a relation as a function?
- How would you represent a relation that is not a function in a graph or table?
- Can all mappings be visualized effectively using diagrams or graphs?
Tip: When analyzing whether a relation is a function, always check if each input () maps to only one output ().
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Math Problem Analysis
Mathematical Concepts
Functions
Relations
Vertical Line Test
Mappings
Formulas
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Theorems
Vertical Line Test
Suitable Grade Level
Grades 8-10