Final answer:
The smallest element in the range of the given relation is -3, which is found by identifying the least 'y-value' from the set of second elements in each ordered pair.
Step-by-step explanation:
The question asks to determine the value of the smallest element in the range of the given relation. The relation provided is a set of ordered pairs: {(0,1),(1,3),(2,2),(3,5),(4,2),(5,-3), (6, 2)}. The range of a relation is the set of all second elements in the ordered pairs, also known as the 'y-values'. We need to identify the smallest 'y-value' from this set.
To find the smallest element in the range, we look at the second value in each ordered pair and determine which one is the least. From the given pairs, the 'y-values' are 1, 3, 2, 5, 2, -3, and 2. The smallest of these values is -3.
Therefore, the smallest element in the range of the relation is -3.