Question

which relation shown is not a function?

Answer 1

The last one is not a function. A function only has one x-value paired to a corresponding y-value. If you have multiple x-values paired to the same y-value that is not a function. In this case you have a vertical line and a vertical line is an invalid function. Also could do the vertical line test if you graphed it and the vertical line you anywhere where the graph if (being just itself) hits the graph in more then one spot (given that the vertical line test is the graph itself)

Answer 2

whenever you have two points that have the same x coordinate, but different y coordinate, is when you don't have a function