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Chapter 1: Problem 3

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(3,4),(3,5),(4,4),(4,5)\\}$$

Short Answer

Expert verified
The relation \(\{(3,4),(3,5),(4,4),(4,5)\}\) is not a function. The domain of the relation is {3,4} and the range of the relation is {4,5}.

Step by step solution

01

Determine whether the relation is a function

Inspect the given set \(\{(3,4),(3,5),(4,4),(4,5)\}\). Observe that the input '3' is related to two outputs: '4' and '5'. Similarly, '4' is also linked to two outputs. As mentioned earlier, in a function, an input cannot link to more than one output. Therefore, this relation is not a function.
02

Identifying Domain and Range

The domain of a relation is the set of all inputs and the range is the set of all outputs. From the given relation \(\{(3,4),(3,5),(4,4),(4,5)\}\), the domain (inputs) can be seen as {3,4} and the range (outputs) is {4,5}.

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