Math Problem Statement

Find the domain and range of each graph based on the provided visual representation.

Solution

From the graph provided, I will extract the domain and range:

  1. Domain (D): The domain refers to the set of all possible xx-values for which the graph exists. In this case:

    • The graph starts at x=3x = -3 (inclusive, closed circle) and ends at x=3x = 3 (inclusive, closed circle).
    • So, the domain is: D:[3,3]D: [-3, 3].
  2. Range (R): The range refers to the set of all possible yy-values for which the graph exists.

    • The graph’s lowest point is y=2y = -2, and its highest point is y=2y = 2.
    • So, the range is: R:[2,2]R: [-2, 2].

Would you like further details or assistance?


Related Questions:

  1. What happens to the domain and range if the graph is extended beyond x=3x = 3?
  2. How do you determine domain and range when there are open circles on the graph?
  3. Can a graph have a domain but no range? Explain why or why not.
  4. How do transformations like shifts affect the domain and range of a graph?
  5. What is the relationship between domain and range for inverse functions?

Tip:

Always pay attention to open versus closed circles on a graph—they indicate whether endpoints are included or excluded in the domain or range!

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Graph Analysis

Formulas

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Theorems

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Suitable Grade Level

Grade 8-10