Problem 3 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

The given relation is not a function, as the same input gives multiple outputs. The domain is \{3, 4\} and the range is \{4, 5\}.

Step 1 - Identify whether the relation is a function

Examine each ordered pair in the relation. In the given relation, we have the pairs (3,4),(3,5),(4,4),(4,5). If an 'x' value (the first number in the pair) is repeated with different 'y' values (the second number in the pair), the relation is not a function. Here, 3 is paired with both 4 and 5, and 4 is paired with both 4 and 5. Therefore, this relation is not a function.

Step 2 - Determine the domain

The domain of a relation consists of all 'x' values, i.e., the first elements in the ordered pairs. Even though the relation is not a function, we can still identify the domain. In this case, the domain is \{3, 4\}, obtained from the first elements of each ordered pair.

Step 3 - Determine the range

The range of a relation consists of all 'y' values, i.e., the second elements in the ordered pairs. In this case, the range is \{4, 5\}, obtained from the second elements of each ordered pair.