Math Problem Statement
Use the graph of the function to find its domain and range. Write the domain and range in interval notation.
Solution
The graph shown represents a function with its domain and range in need of identification.
Domain:
The domain represents the set of all possible x-values (horizontal axis) that the function can take. From the graph:
- The leftmost point on the curve appears to be at , and the rightmost point is at .
- The point at is a closed point (filled in), meaning that is included.
- The point at is an open point (hollow), meaning that is not included.
Thus, the domain in interval notation is:
Range:
The range represents the set of all possible y-values (vertical axis) that the function takes. From the graph:
- The lowest point on the curve is at , and the highest point is at .
- At , the point is closed (included), and at , the point is open (excluded).
Thus, the range in interval notation is:
Final Answer:
- Domain:
- Range:
Do you want more details or have any questions?
Here are 5 related questions you might want to explore:
- How do you determine if a point is open or closed on a graph?
- What is the significance of interval notation in calculus?
- How would the domain and range change if the graph extended further?
- Can a function have an infinite range or domain? What would that look like?
- How does continuity of the function affect its domain and range?
Tip: Closed intervals like include the endpoints, while open intervals exclude them.
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Math Problem Analysis
Mathematical Concepts
Graphing
Functions
Domain and Range
Interval Notation
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12