Math Problem Statement

Is this relation a function?

Solution

The graph presented shows two lines that cross each other. To determine if this relation is a function, we can apply the Vertical Line Test.

This test states that a relation is a function if and only if no vertical line intersects the graph at more than one point.

In the given graph, if we draw a vertical line at various points along the x-axis, particularly where the lines intersect (around the center), the vertical line would pass through more than one point. This indicates that there are multiple y-values for the same x-value at that intersection.

Conclusion: The relation is not a function because it fails the vertical line test.

Would you like more details on the vertical line test or further clarification?


Here are some related questions for further practice:

  1. What is the vertical line test and how does it work?
  2. How do you determine the domain and range of a function from a graph?
  3. What are examples of relations that are not functions?
  4. Can a function have multiple x-values for the same y-value?
  5. How would the graph change if it were a function?

Tip: Always use the vertical line test when analyzing a graph to check if it represents a function!

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Math Problem Analysis

Mathematical Concepts

Functions
Relations
Vertical Line Test

Formulas

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Theorems

Vertical Line Test

Suitable Grade Level

Grades 8-10