Math Problem Statement

What is the domain and range

What is the domain and range?

Solution

To determine the domain and range of the function shown in the graph, let's analyze the plot.

Domain:

The domain is the set of all possible x-values that the function can take.

Looking at the graph:

  • The graph starts at x=3x = 3 and continues to the right until x=4x = 4.
  • Both endpoints seem to be included in the function, so the domain will include these values.

Domain:

[3,4][3, 4]

Range:

The range is the set of all possible y-values the function can output.

  • The lowest point on the graph is near y=0y = 0, and the highest point is near y=4y = 4.

Range:

[0,4][0, 4]

The domain is from x=3x = 3 to x=4x = 4, and the range is from y=0y = 0 to y=4y = 4.

Would you like more details or clarifications on the domain and range? Here are a few related questions to expand on this concept:

  1. What happens to the domain and range if the endpoints are not included?
  2. How can we identify if the graph has a discontinuity affecting domain or range?
  3. What is the difference between open and closed intervals in domain and range?
  4. How would the domain and range change for a function like a parabola?
  5. How do we express domain and range for periodic functions?

Tip: When determining domain and range from a graph, always check if the endpoints are included (solid dots) or excluded (open dots) to accurately represent the intervals.

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Math Problem Analysis

Mathematical Concepts

Functions
Domain and Range
Graph Interpretation

Formulas

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Theorems

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Suitable Grade Level

Grades 8-10