Math Problem Statement

Find the domain and the range of the relation shown on the graph. Use the vertical line test to determine whether the graph is the graph of a function.

Solution

The problem asks to find the domain and range of the relation shown in the graph and to determine if it represents a function using the vertical line test.

Step 1: Vertical Line Test

The vertical line test determines whether a graph represents a function. A graph is a function if no vertical line intersects the graph at more than one point. In this graph, there appears to be a horizontal line, which would pass the vertical line test because any vertical line would only touch it once. Therefore, the graph represents a function.

Step 2: Domain of the Relation

The domain is the set of all possible values of xx (horizontal axis) for which the graph exists.

  • From the graph, the horizontal line stretches between x=10x = -10 and x=10x = 10.
  • Therefore, the domain is the interval [10,10][-10, 10].

So, the correct answer for the domain (Choice B) is: [10,10][-10, 10]

Would you like details on the range, or do you have any other questions?

Related Questions:

  1. What is the range of this function?
  2. Can a horizontal line ever fail the vertical line test?
  3. How do you find the range from a graph?
  4. What is the difference between a relation and a function?
  5. How do you write a domain in set notation?

Tip: When analyzing a graph, always carefully observe the points where the graph begins and ends to determine the domain and range.

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Math Problem Analysis

Mathematical Concepts

Functions
Domain and Range
Vertical Line Test

Formulas

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Theorems

Vertical Line Test

Suitable Grade Level

Grades 9-12