Math Problem Statement
Solution
To determine which of these graphs is not a function, we can use the Vertical Line Test. This test states that if a vertical line intersects a graph at more than one point, the graph does not represent a function.
Let's examine each graph based on this rule:
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First Graph (Top Graph with Triangle): This graph passes the vertical line test, as each vertical line crosses the graph at only one point. This is a function.
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Second Graph (Middle Graph with Crossing Lines): This graph does not pass the vertical line test. For example, vertical lines at certain x-values intersect the graph at two points, indicating that this is not a function.
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Third Graph (Parabola): This graph passes the vertical line test, as any vertical line crosses the graph at only one point. This is a function.
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Fourth Graph (Exponential Curve): This graph also passes the vertical line test, as each vertical line intersects the graph at only one point. This is a function.
Conclusion:
The second graph does not represent a function because it fails the vertical line test. Therefore, the correct answer is the second option.
Would you like further details or have any questions?
Related Questions:
- What is the Vertical Line Test, and why does it work?
- How can you tell if a graph represents a function without plotting it?
- Can a graph represent a relation that is not a function? Explain with examples.
- What distinguishes a function from a general relation?
- How do horizontal lines affect whether a graph represents a function?
Tip:
For any graph, remember that a function will have only one output for each input, which visually translates to passing the Vertical Line Test.
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Math Problem Analysis
Mathematical Concepts
Functions
Vertical Line Test
Graph Interpretation
Formulas
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Theorems
Vertical Line Test
Suitable Grade Level
Grades 7-9
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