Math Problem Statement

Which relation is a function?

Responses

Number graph ranging from negative four to four on the x and y axes. Points are drawn on the graph at begin ordered pair negative three comma negative one end ordered pair and begin ordered pair negative two comma three end ordered pair and begin ordered pair zero comma negative three end ordered pair and begin ordered pair one comma negative two end ordered pair and begin ordered pair two comma two end ordered pair and begin ordered pair three comma zero end ordered pair Image with alt text: Number graph ranging from negative four to four on the x and y axes. Points are drawn on the graph at begin ordered pair negative three comma negative one end ordered pair and begin ordered pair negative two comma three end ordered pair and begin ordered pair zero comma negative three end ordered pair and begin ordered pair one comma negative two end ordered pair and begin ordered pair two comma two end ordered pair and begin ordered pair three comma zero end ordered pair

Number graph ranging from negative four to four on the x and y axes. Points are drawn on the graph at begin ordered pair negative four comma three end ordered pair and begin ordered pair negative two comma one end ordered pair and begin ordered pair negative one comma three end ordered pair and begin ordered pair negative one comma negative one end ordered pair and begin ordered pair one comma one end ordered pair and begin ordered pair two comma negative one end ordered pair Image with alt text: Number graph ranging from negative four to four on the x and y axes. Points are drawn on the graph at begin ordered pair negative four comma three end ordered pair and begin ordered pair negative two comma one end ordered pair and begin ordered pair negative one comma three end ordered pair and begin ordered pair negative one comma negative one end ordered pair and begin ordered pair one comma one end ordered pair and begin ordered pair two comma negative one end ordered pair

Number graph ranging from negative four to four on the x and y axes. Points are drawn on the graph at begin ordered pair negative two comma one end ordered pair and begin ordered pair negative two comma negative two end ordered pair and begin ordered pair negative one comma three end ordered pair and begin ordered pair zero comma one end ordered pair and begin ordered pair two comma zero end ordered pair and begin ordered pair two comma negative two end ordered pair

Image with alt text: Number graph ranging from negative four to four on the x and y axes. Points are drawn on the graph at begin ordered pair negative two comma one end ordered pair and begin ordered pair negative two comma negative two end ordered pair and begin ordered pair negative one comma three end ordered pair and begin ordered pair zero comma one end ordered pair and begin ordered pair two comma zero end ordered pair and begin ordered pair two comma negative two end ordered pair

Number graph ranging from negative four to four on the x and y axes. Points are drawn on the graph at begin ordered pair negative two comma one end ordered pair and begin ordered pair negative one comma three end ordered pair and begin ordered pair zero comma two end ordered pair and begin ordered pair zero comma negative one end ordered pair and begin ordered pair one comma three end ordered pair and begin ordered pair two comma one end ordered pair

Solution

To determine which relation is a function, we need to check if each graph satisfies the vertical line test. This test states that a relation is a function if no vertical line intersects the graph at more than one point. In other words, each input (x-value) must correspond to exactly one output (y-value).

Let's analyze each graph:

Graph 1

  • Points: (-3, -1), (-2, 3), (0, -3), (1, -2), (2, 2), (3, 0)
  • Test: Each x-value corresponds to exactly one y-value. Thus, this is a function.

Graph 2

  • Points: (-4, 3), (-2, 1), (-1, 3), (-1, -1), (1, 1), (2, -1)
  • Test: The x-value of -1 has two different y-values (3 and -1). This means the graph fails the vertical line test, so this is not a function.

Graph 3

  • Points: (-2, 1), (-2, -2), (-1, 3), (0, 1), (2, 0), (2, -2)
  • Test: The x-values -2 and 2 have two different y-values each. This fails the vertical line test, so this is not a function.

Graph 4

  • Points: (-2, 1), (-1, 3), (0, 2), (0, -1), (1, 3), (2, 1)
  • Test: The x-value of 0 has two different y-values (2 and -1), so this is not a function.

Conclusion:

  • Only Graph 1 represents a function because it passes the vertical line test.

Do you need further clarification on any of the graphs or the vertical line test? Here are some related questions:

  1. How does the vertical line test help in identifying functions?
  2. What is the difference between a relation and a function?
  3. Can you give an example of a real-world situation modeled by a function?
  4. How do you express a function using a formula or equation?
  5. How can functions be represented in tabular form?

Tip: When analyzing functions, always ensure that each input has exactly one output to maintain the function property.

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Math Problem Analysis

Mathematical Concepts

Functions
Relations
Graph Analysis
Vertical Line Test

Formulas

-

Theorems

Vertical Line Test

Suitable Grade Level

Grades 9-12

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