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Chapter 1: Problem 10

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

Short Answer

Expert verified
Yes, the given relation is a function. The domain is \(\{4, 5, 6\}\) and the range is \(\{1\}\).

Step by step solution

01

Identify if the Relation is a Function

A relation is a function if each input (x values) has exactly one output (y values). Looking at the relation \(\{(4,1),(5,1),(6,1)\}\), it can be seen that all x-values have unique y-values. Therefore, this relation is a function.
02

Determine the Domain

The domain of a function refers to all possible input values (x-values). For the given function, the domain is \(\{4, 5, 6\}\).
03

Find the Range

The range of a function is the set of all possible output values (y-values), which are influenced by the x-values. In this case, since all x-values lead to the same y-value (1), the range is \(\{1\}\).

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