Math Problem Statement
Give the domain and range of the function shown in the graph.
Solution
From the given graph:
Domain:
The domain of a function includes all possible -values for which the function is defined. From the graph, the function is defined for all . Thus, the domain is:
Range:
The range of a function includes all possible -values that the function outputs. From the graph, the function outputs all values . Thus, the range is:
Let me know if you need further explanation or clarification on this!
Follow-up Questions:
- What does it mean for a function to have a restricted domain or range?
- How can you determine the domain and range of more complex graphs?
- What are common characteristics of functions with vertical asymptotes?
- Can you explain the significance of the point where the function approaches but does not cross the axis?
- How do transformations (e.g., shifts) affect the domain and range of a function?
Tip: Always pay attention to the behavior near boundaries or asymptotes when determining domain and range.
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Math Problem Analysis
Mathematical Concepts
Domain and Range
Functions
Graph Analysis
Formulas
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Theorems
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Suitable Grade Level
Grades 8-10