Math Problem Statement
Write the domain and range of the graph shown using inequalities.
Solution
To determine the domain and range of the graph, let's analyze it based on the curve you provided:
Domain (x-values):
The domain consists of all possible x-values that the graph covers horizontally. From the graph:
- The leftmost point occurs at (closed circle), indicating the graph starts from there.
- The rightmost point occurs at (closed circle), meaning the graph extends up to this point.
Thus, the domain is .
Range (y-values):
The range consists of all possible y-values that the graph covers vertically. From the graph:
- The highest point is at , corresponding to the point at .
- The lowest point is at , corresponding to the vertex of the parabola.
Thus, the range is .
Final answer:
- Domain:
- Range:
Do you want more details or have any questions about how to interpret the graph?
Here are 5 questions to expand your understanding:
- How do you determine if a point is included or excluded from a domain or range?
- How can you tell the domain of a function by looking at a graph?
- What is the difference between a closed and open circle on a graph?
- How would the domain and range change if the parabola were wider?
- Can you think of real-world situations where domain and range are used?
Tip: Always look at both endpoints of a graph and whether the points are open or closed to determine the exact domain and range!
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Math Problem Analysis
Mathematical Concepts
Domain and Range
Graph Analysis
Parabolas
Formulas
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Theorems
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Suitable Grade Level
Grades 8-10