Math Problem Statement

find the domain and range

Solution

To find the domain and range of the given function based on the graph:

Domain:

The domain refers to all the possible xx-values that the function can take.

  • The graph starts at x=3x = -3 and ends at x=2x = 2.
  • The point at x=3x = -3 is filled in (solid dot), indicating that x=3x = -3 is included in the domain.
  • The point at x=2x = 2 is open (hollow dot), indicating that x=2x = 2 is not included in the domain.

So, the domain of the function is: Domain: [3,2)\text{Domain: } [-3, 2)

Range:

The range refers to all the possible yy-values that the function can take.

  • The highest point on the graph is at y=4y = 4 when x=3x = -3 (filled dot).
  • The lowest point on the graph is at y=4y = -4 when x=2x = 2 (open dot).

So, the range of the function is: Range: [4,4]\text{Range: } [-4, 4]

Summary:

  • Domain: [3,2)[-3, 2)
  • Range: [4,4][-4, 4]

Would you like further details or have any questions? Here are some related questions to explore further:

  1. What does it mean for a function to have a closed interval in its domain or range?
  2. How would the domain and range change if the graph were shifted vertically or horizontally?
  3. Can you identify whether the function is increasing or decreasing over its domain?
  4. What are the implications of having an open or closed endpoint in the domain or range?
  5. How would the domain and range differ if this function were extended beyond the given graph?

Tip: When determining the domain and range from a graph, always check for open and closed points to understand whether endpoints are included or excluded.

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Math Problem Analysis

Mathematical Concepts

Functions
Domain and Range

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12