Problem 4 - Introductory Algebra for College Students

Question

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(5,6),(5,7),(6,6),(6,7)\\}$$

Step-by-Step Solution

Answer

The given relation is not a function. The domain is {5, 6} and the range is {6,7}.

Step 1: Determine if the relation is a function

Observe each pair in the relation. In a function, each input (x-value or first element of the pair) can have only one output (y-value or second element). In this relation, the pair (5,6) and (5,7) reveal that the input '5' corresponds to two different outputs '6' and '7'. Therefore, this relation is not a function.

Step 2: Find the domain

The domain of a relation is the set of all inputs or the first elements of the ordered pairs. In this relation, looking at all the first elements of the pairs gives the domain: {5, 6}.

Step 3: Determine the range

The range of a relation consists of all outputs or the second elements of the ordered pairs. From this relation, gathering all the second elements of the pairs provides the range: {6,7}.