Math Problem Statement
Find the range.
Solution
To find the range of the function depicted in the graph, let's analyze the y-values the graph covers:
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From to : The function is a horizontal line at but is not defined at due to the open circle, so is included.
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At : There is a filled point at . So, is included.
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From to : The function decreases linearly, covering values from to . Both endpoints are included as filled points.
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At : The function is defined at .
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From to : The function dips to a minimum at approximately .
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At : There is an open circle at , so is not included here.
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For : The function rises quickly, covering all values greater than .
Range:
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Here are five related questions:
- How would you find the domain of this graph?
- What type of discontinuities does the graph have?
- How do the open and closed circles affect the range?
- How can you determine intervals of increase and decrease from the graph?
- What is the minimum value of the function, and where does it occur?
Tip: When finding the range of a graph, pay close attention to open and closed circles, as they indicate whether endpoints are included or excluded.
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Math Problem Analysis
Mathematical Concepts
Function Range
Graph Interpretation
Discontinuities
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12