my question is about math ca

Question

Zach lists the following relation and tells his teacher it is a function. {(2, 1) (3, - 2) (4, 5) (5, - 2)}. He is correct. His teacher instructs him to add another ordered pair so that it will NOT be a function. Which of the following ordered pairs should Zach add?

Answer 1

Hello Mni. A set of points or a line, when drawn, is a function if it passes the Vertical Line test. This means that once drawn, you can draw a vertical line at any point and only touch the line once. If you draw the vertical line and touch the line at more than one point, it fails the Vertical Line Test and is not a function. The set of points given is a function because for every x value, there is only one y value appointed to it. For example, for the first point, it has an x value of 2. In none of the other points is there another x value of 2, meaning for this point it follows the rules of a function. You can repeat the process with the other points and you can conclude that the points do indeed compose a function. To make these points not a function, all you have to do is give a point with one of the x values given and simply appoint a different y value than the one given. For example, if you use the first x value, all you have to write is (2, 0), (2,3), (2, -45), (2,100), etc. You can choose any of the other x values as well; (3,0), (4,59), (5,23) and so forth. Hope this helped, and good luck!