Problem 2 - Precalculus Essentials

Question

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(4,5),(6,7),(8,8)\\}$$

Step-by-Step Solution

Answer

Yes, the relation is a function. The domain is \(D=\{4,6,8\}\) and the range is \(R=\{5,7,8\}\).

Step 1: Verify if the relation is a function

The relation given is \\{(4,5),(6,7),(8,8)\\}. Looking at each pair, it can be seen that each x-value is linked to exactly one y-value, hence this relation is indeed a function.

Step 2: Determining the domain and range

For domain, list all distinct x-values from the ordered pairs. The x-values are 4, 6, and 8. So, the domain is \(D=\{4,6,8\}\). For range, list all distinct y-values from the ordered pairs. The y-values are 5, 7, and 8.Therefore, the range is \(R=\{5,7,8\}\).