Math Problem Statement

Solve the

Solution

The image shows a graph of a function, and the task is to find the domain and range of the function.

Domain:

The domain of a function is the set of all possible input values (x-values) for which the function is defined. In the graph:

  • The graph starts at x=3x = -3 and ends at x=2x = 2.
  • Therefore, the domain is [3,2][-3, 2].

Range:

The range of a function is the set of all possible output values (y-values) that the function can take.

  • The highest point on the graph occurs at y=3y = 3.
  • The lowest point occurs at y=2y = -2.
  • Therefore, the range is [2,3][-2, 3].

Answer:

  • Domain: [3,2][-3, 2]
  • Range: [2,3][-2, 3]

Would you like any further details or explanations?

Here are five related questions to deepen your understanding:

  1. How does one determine the domain and range from a graph with open or closed endpoints?
  2. What is the importance of the domain and range in defining a function?
  3. How would the domain and range change if the graph had arrows extending infinitely?
  4. Can the domain of a function be a discrete set of points? Give an example.
  5. How does the concept of domain and range apply to real-world situations?

Tip: When determining the domain and range from a graph, carefully observe the endpoints and whether they are included (closed dot) or not (open dot).

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Math Problem Analysis

Mathematical Concepts

Functions
Graphing
Domain and Range

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12