Math Problem Statement
Find the domain and range of the function shown.
Solution
Domain and Range of the Function:
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Domain: The domain represents all the possible input values (x-values) for the function.
- The graph starts from the left at (indicated by the open circle), meaning this point is not included in the domain.
- The graph continues until (indicated by the closed circle), meaning this point is included in the domain.
Therefore, the domain is:
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Range: The range represents all the possible output values (y-values) for the function.
- The highest point on the graph is around , which is not included (open circle).
- The lowest point on the graph is , which is included (closed circle).
Therefore, the range is:
Would you like more details or have any questions?
Here are 5 related questions:
- How do you find the domain and range of a function algebraically?
- What is the difference between open and closed intervals in domain and range?
- How do you determine if a function is continuous based on its graph?
- How can you identify whether a function is increasing or decreasing from a graph?
- What is the significance of the domain and range in real-world applications?
Tip: When determining the domain and range of a function from a graph, always pay attention to open and closed circles, as they indicate whether specific values are included or not.
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Math Problem Analysis
Mathematical Concepts
Domain and Range
Functions
Graph Analysis
Formulas
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Theorems
Understanding Open and Closed Intervals
Suitable Grade Level
Grades 9-11