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Chapter 1: Problem 6

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(10,4),(-2,4),(-1,1),(5,6)\\}$$

Short Answer

Expert verified
The given relation is a function. Its domain is \{\(10, -2, -1, 5\)\} and its range is \{\(4, 1, 6\)\}.

Step by step solution

01

Determine if relation is a function

Check each input and make sure it does not map to more than one output. In this relation, each input - 10, -2, -1, 5 - maps to exactly one output. Therefore, it is a function.
02

Find the domain

The domain of a relation is the set of all inputs. In this case, the inputs are the first components of each ordered pair, which are 10, -2, -1, and 5. Hence, the domain is \{\(10, -2, -1, 5\)\}
03

Find the range

The range of a relation is the set of all outputs. In this case, the outputs are the second components of each ordered pair, which are 4, 4, 1, and 6. Since repetition does not count in sets, the range is \{\(4, 1, 6\)\}

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