Math Problem Statement

Given a graph with several plotted points, determine the domain and range.

Solution

The graph you provided shows several points plotted on a coordinate plane. From this, we can determine the domain and range of the set of points.

  • Domain: The domain consists of all the x-values of the points in the graph.
  • Range: The range consists of all the y-values of the points in the graph.

Let’s analyze the points:

  • The first point is at (3,3)(-3, 3).
  • The second point is at (0,4)(0, 4).
  • The third point is at (2,1)(2, 1).
  • The fourth point is at (1,1)(1, -1).
  • The fifth point is at (0,3)(0, -3).

Domain:

The domain is the set of x-values: {3,0,2,1}\{-3, 0, 2, 1\}. Since 00 appears twice, it only needs to be listed once. Therefore, the domain is: {3,0,1,2}\{-3, 0, 1, 2\}

Range:

The range is the set of y-values: {3,4,1,1,3}\{3, 4, 1, -1, -3\}. So, the range is: {3,1,1,3,4}\{-3, -1, 1, 3, 4\}

Final Answer:

  • Domain: {3,0,1,2}\{-3, 0, 1, 2\}
  • Range: {3,1,1,3,4}\{-3, -1, 1, 3, 4\}

Would you like more details, or do you have any questions?

Here are 5 related questions you could explore:

  1. What is the significance of domain and range in a function?
  2. How do you determine if a set of points represents a function?
  3. Can a domain have repeated values in a function?
  4. What changes in the graph if we reflect the points across the y-axis?
  5. How would the range change if we added more points to the graph?

Tip: When graphing points, always organize the coordinates systematically to easily extract the domain and range!

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Domain
Range

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8