Math Problem Statement
State the domain and range for each graph and then tellif the graph is a function (wite yes or no). In set builder notation
Solution
Let's analyze the two graphs shown in the image:
Left Graph:
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Domain: The domain is the set of all possible x-values. The graph is a vertical line at . Therefore, the domain is:
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Range: The range is the set of all possible y-values. Since the vertical line extends infinitely in both directions along the y-axis, the range is all real numbers:
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Is it a function?: No, this graph is not a function. A vertical line test would show that multiple y-values correspond to the single x-value of , which violates the definition of a function.
Right Graph:
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Domain: The domain is the set of all possible x-values. The graph is a single point at . Therefore, the domain is:
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Range: The range is the set of all possible y-values. The graph is a single point at . Therefore, the range is:
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Is it a function?: Yes, this graph is a function. Each x-value corresponds to exactly one y-value.
Would you like any further details or explanations?
Related Questions:
- What is the vertical line test, and how does it determine if a graph is a function?
- Can a single point on a graph ever not be a function?
- How does the domain differ when dealing with parabolas or quadratic functions?
- What happens to the domain and range when the graph of a function is shifted horizontally or vertically?
- What is the difference between a continuous and a discrete domain?
Tip:
When determining if a graph is a function, always remember that for each x-value, there should be only one corresponding y-value.
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Math Problem Analysis
Mathematical Concepts
Functions
Domain and Range
Vertical Line Test
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12
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