Math Problem Statement

Which of these graphs is not a function?

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:

  1. 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.

  2. 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.

  3. 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.

  4. 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:

  1. What is the Vertical Line Test, and why does it work?
  2. How can you tell if a graph represents a function without plotting it?
  3. Can a graph represent a relation that is not a function? Explain with examples.
  4. What distinguishes a function from a general relation?
  5. 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