Question

Which relation is a function? A. {(8,3), (-1,-1), (8,7), (-1,7)} B. {(1,6), (2,-3), (2,7), (3,7)} C. {(-3,6), (-3,9), (-1,4), (0,3)} D. {(4,7), (-9,3), (0,3), (2,2)}

Answer 1

A. Not a function since x = 8 repeats. We have x = 8 pair up with y = 3 and y = 7 at the same time.

B. Not a function for similar reasons. Now x = 2 repeats. We have x = 2 pair up with y = -3 and y = 7

C. Not a function. We have x = -3 pair up with both y = 6 and y = 9 at the same time.

D. This is a function. Each x value is listed once and only once. Any input (x) leads to exactly one output (y). For choices A through C, it is possible to draw a vertical line through more than one point, thereby failing the vertical line test. In choice D, it is not possible to draw a vertical line through more than one point of this list. So this relation passes the vertical line test.

Answer: Choice D