Math Problem Statement
Determine the range of the following graph:
Solution
The task is to determine the range of the given graph.
Step-by-step solution:
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Definition of Range: The range of a function is the set of all possible -values (outputs) that the function can take. To find the range, observe the vertical extent of the graph.
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Analyzing the Graph:
- The graph has a minimum -value at approximately (the lowest point of the curve).
- The graph extends upwards to a maximum -value of , as indicated by the open circle near .
- The open circle at shows that is not included in the range.
- The graph continues smoothly between and , so all -values in this interval are included except .
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Conclusion: The range of the graph is: This means can take any value from to , including but excluding .
Do you have any questions or want further clarification?
Related Questions:
- What is the difference between the range and domain of a function?
- How would the range change if the open circle at were filled?
- Can the range of a graph include gaps or discontinuities? Explain with examples.
- How can you determine if a graph has an open or closed interval for its range?
- How does the behavior of the graph near the edges influence the range?
Tip:
When identifying the range of a function, always check for open or closed points and note whether the graph extends infinitely or is bounded within a specific interval.
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Math Problem Analysis
Mathematical Concepts
Range of a Function
Graphs of Functions
Formulas
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Theorems
Range Definition
Suitable Grade Level
Grades 9-11