Question

1. explain why the relation shown in the table below is a function.

x	-1	0	1	2
y	2	4	4	5

complete the table below with values for both x and y so that this new relation is not a function.

x	-1	0	1	2	6
y	2	4	4	5	7

Explanation:

Part 1: Why the relation is a function

A function is a relation where each input (x - value) has exactly one output (y - value). In the given table, the x - values are - 1, 0, 1, 2. For x=-1, y = 2 (only one y - value); for x = 0, y = 4 (only one y - value); for x = 1, y = 4 (only one y - value); for x = 2, y = 5 (only one y - value). So each x - value is paired with exactly one y - value, which satisfies the definition of a function.

Part 2: Completing the table to make it not a function

To make a relation not a function, we need to have at least one x - value paired with more than one y - value. Let's take an existing x - value, say x=-1. Currently, when x=-1, y = 2. If we add a new row with x=-1 and a different y - value, say y = 3, then the x - value - 1 will be paired with two different y - values (2 and 3), and the relation will not be a function. So we can complete the table as follows:

x	-1	0	1	2	-1

(Note: We could also use other existing x - values like x = 0, x = 1, or x = 2 and give them a different y - value. For example, if we take x = 0 and set y = 5 (different from the existing y = 4 for x = 0), the relation will also not be a function.)

Answer:

• The given relation is a function because each x - value (-1, 0, 1, 2) is associated with exactly one y - value.
• One way to complete the table to make it not a function is:

x	-1	0	1	2	-1

(Other valid completions exist, such as using an existing x - value and a new y - value for that x - value.)