Math Problem Statement
find the domain and range
Solution
To find the domain and range of the given function based on the graph:
Domain:
The domain refers to all the possible -values that the function can take.
- The graph starts at and ends at .
- The point at is filled in (solid dot), indicating that is included in the domain.
- The point at is open (hollow dot), indicating that is not included in the domain.
So, the domain of the function is:
Range:
The range refers to all the possible -values that the function can take.
- The highest point on the graph is at when (filled dot).
- The lowest point on the graph is at when (open dot).
So, the range of the function is:
Summary:
- Domain:
- Range:
Would you like further details or have any questions? Here are some related questions to explore further:
- What does it mean for a function to have a closed interval in its domain or range?
- How would the domain and range change if the graph were shifted vertically or horizontally?
- Can you identify whether the function is increasing or decreasing over its domain?
- What are the implications of having an open or closed endpoint in the domain or range?
- How would the domain and range differ if this function were extended beyond the given graph?
Tip: When determining the domain and range from a graph, always check for open and closed points to understand whether endpoints are included or excluded.
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Math Problem Analysis
Mathematical Concepts
Functions
Domain and Range
Formulas
-
Theorems
-
Suitable Grade Level
Grades 9-12