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Domain And Range Of Relation:
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The domain of a relation is the set of all first elements (x-coordinates) from the ordered pairs, while the range is the set of all second elements (y-coordinates). For a relation R, Domain = {x | (x,y) ∈ R} and Range = {y | (x,y) ∈ R}.
The calculator uses the mathematical definition:
Process: The calculator parses the input relation, extracts all unique x-values for the domain and all unique y-values for the range, then returns both sets in sorted order.
Details: Determining domain and range is fundamental in mathematics, particularly in functions and relations analysis. It helps identify valid inputs and possible outputs, which is crucial for understanding mathematical relationships and their applications.
Tips: Enter the relation as ordered pairs in the format (x1,y1),(x2,y2),(x3,y3). Ensure proper parentheses and comma separation. The calculator will automatically extract and display the domain and range.
Q1: What's the difference between domain and range?
A: Domain represents all possible input values (x-coordinates), while range represents all possible output values (y-coordinates) in a relation.
Q2: How should I format the relation input?
A: Use the format (x1,y1),(x2,y2),(x3,y3) with parentheses around each ordered pair and commas separating the pairs.
Q3: Does the calculator handle duplicate values?
A: Yes, duplicate x or y values are automatically filtered to show only unique values in the domain and range sets.
Q4: Can I use this for functions as well as relations?
A: Yes, since all functions are relations, this calculator works for both functions and general relations.
Q5: What if my relation contains non-numeric values?
A: The calculator can handle both numeric and non-numeric values, as it treats all inputs as strings for domain and range extraction.