Question

Table 1 is a table of ordered pairs (a tabular representation of a relation between X and Y). It is a function because each X-value (4, 5, 6) corresponds to exactly one Y-value.

Table 2 is a table of ordered pairs (a tabular representation of a relation between X and Y). It is not a function because the X-value 3 corresponds to two different Y-values (4 and 5).

Answer 1

Your statements are correct.

- Definition: A relation is a function when each input (X-value) corresponds to exactly one output (Y-value).
- Table 1: Is a function because each X (4, 5, 6) appears exactly once (or maps to exactly one Y).
- Table 2: Is not a function because the X-value 3 maps to two different Y-values (4 and 5), so a single input has more than one output.

Notes:
- It’s fine for different X-values to share the same Y-value and still be a function (e.g., (1,2) and (2,2) is allowed).
- To make Table 2 a function you could remove one of the pairs with X = 3 or change one of those pairs so 3 appears only once.