Question

graph the ordered pairs from the table. determine if the relation is a function.

x	y
-1	3
1	-1
2	2
1	3

(there are some graphs and options below, but the specific content of the graphs and options is partially obscured, and the main text is as above.)

Explanation:

Step1: Recall the definition of a function

A relation is a function if each input (x - value) has exactly one output (y - value). In other words, no two ordered pairs in the relation can have the same x - value with different y - values.

Step2: Analyze the given table

The ordered pairs from the table are \((- 1,3)\), \((1,-1)\), \((2,2)\), and \((1,3)\). We can see that the x - value \(x = 1\) is paired with \(y=-1\) and \(y = 3\).

Step3: Determine if it is a function

Since the input \(x = 1\) has more than one output (\(-1\) and \(3\)), the relation does not satisfy the definition of a function.

For graphing the ordered pairs:

• For the point \((-1,3)\), we move 1 unit to the left of the origin on the x - axis and 3 units up on the y - axis.
• For the point \((1,-1)\), we move 1 unit to the right of the origin on the x - axis and 1 unit down on the y - axis.
• For the point \((2,2)\), we move 2 units to the right of the origin on the x - axis and 2 units up on the y - axis.
• For the point \((1,3)\), we move 1 unit to the right of the origin on the x - axis and 3 units up on the y - axis.

When we graph these points, we can see that the x - value \(x = 1\) has two different y - values plotted, which also shows that it is not a function.

Answer:

The relation is not a function because the x - value \(1\) is associated with two different y - values (\(-1\) and \(3\)). To graph the ordered pairs, plot \((-1,3)\), \((1,-1)\), \((2,2)\), and \((1,3)\) on a coordinate plane.