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Step 1:I'll solve this problem by explaining the domain of a relation step by step:
Step 2:: Definition of Domain
The domain of a relation is the set of all input values (x-values or first coordinates) that are present in the relation. In other words, it is the set of all possible x-values that have a corresponding y-value in the relation.
Step 3:: Identifying Domain in Different Representations
- For a function or relation given as a set of ordered pairs: List all unique x-values - For a function given as an equation: Determine all x-values that make the equation valid - For a graph: Find all x-coordinates of points on the graph
Step 4:: Key Characteristics of Domain
- The domain represents the set of possible input values - It can be finite or infinite - It depends on the specific constraints of the relation or function
Step 5:: Examples of Domain Determination
- $$f(x) = \sqrt{x}$$: Domain is $$\{x | x \geq 0\}$$ (all non-negative real numbers)
- f(x) = \frac{1}{x- 2}: Domain is \{x | x \neq 2\} (all real numbers except 2)
Final Answer
The domain of a relation is the complete set of all possible input values (x-values) that have a corresponding output value in the relation.
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