Problem 10 - Precalculus Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: Determine the Domain

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

Step 3: 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 \(\{1\}\).