Math Problem Statement

For each graph below, determine whether the relation graphed is a function or not.

Solution

To determine whether the graphed relation is a function or not, we use the Vertical Line Test:

  • A graph represents a function if and only if no vertical line intersects the graph at more than one point.

Let’s analyze each graph:

  1. Top Graph: The graph is a parabola. Applying the vertical line test, some vertical lines (e.g., near the vertex) intersect the graph twice. Therefore, this is NOT a function.

  2. Middle Graph: This graph is a curve extending upwards. Some vertical lines will intersect the graph at more than one point (e.g., near the center of the curve). This is NOT a function.

  3. Bottom Graph: This graph is a straight line. Any vertical line intersects the graph only once. This IS a function.

Would you like further clarification or detailed explanations? Let me know if you have more questions!

Here are related questions to deepen your understanding:

  1. What is the definition of a function in mathematics?
  2. How does the vertical line test work for identifying functions?
  3. Are all straight-line graphs always functions? Why or why not?
  4. How can you algebraically confirm if a relation is a function?
  5. Can a relation fail the vertical line test but still have some functional properties?

Tip: Always visualize or sketch graphs if unsure about the vertical line test—it’s an intuitive and reliable method!

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Math Problem Analysis

Mathematical Concepts

Functions
Graphs
Vertical Line Test

Formulas

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Theorems

Vertical Line Test

Suitable Grade Level

Grades 8-10