Graph the relation shown in the table. Is the relation a function? Why or why not?
(-5,-5)
(-3,-3)
(1,1)
(2,2)
Yes; no horizontal line passes through two graphed points.
Yes; no vertical line passes through two graphed points.
No; a vertical line passes through two graphed points.
No; a horizontal line passes through two graphed points.
The relation represented by the table is a function because each input value (x) corresponds to exactly one output value (y). This can be seen by noting that no input value repeats in the table. Since each input value has a unique output value, the relation is a function.
Graphically, the points (-5,-5), (-3,-3), (1,1), and (2,2) would appear as a straight line passing through the origin with a slope of 1. Since each x-value corresponds to only one y-value, no vertical line passes through two points on the graph, confirming that it is a function.