Math Problem Statement
Solution
To determine the domain and range of the function represented by the graph, let's analyze the endpoints and behavior of the graph:
Domain:
The domain represents the set of all possible -values for which the function is defined.
- The graph starts at on the left (open circle, meaning is not included).
- The graph extends to on the right (closed circle, meaning is included).
- Therefore, the domain is .
Range:
The range represents the set of all possible -values that the function takes.
- The graph starts at (open circle, meaning is not included).
- The graph extends to (closed circle, meaning is included).
- Therefore, the range is .
Now, let's look at the answer choices:
- Option D: and doesn't include the lower bound correctly for the -values.
- Option A: and matches the description, except the inequality is incorrect because it's an open circle at .
Thus, the correct answer is Option A.
Would you like any additional details or clarifications?
Here are 5 related questions:
- What is the definition of domain and range in general?
- How do you interpret open and closed circles on a graph?
- What are other methods for finding the range of a function?
- How does one determine if a function is continuous from its graph?
- Can a function have a different domain than range?
Tip: Always check the endpoints of a graph carefully to see whether the points are included (closed circle) or excluded (open circle).
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Math Problem Analysis
Mathematical Concepts
Domain and Range
Function Graphs
Inequalities
Formulas
Domain: set of all possible x-values
Range: set of all possible y-values
Theorems
Understanding open and closed intervals based on graph endpoints
Suitable Grade Level
Grades 8-10