Question

Which relation is a function?

A. {(-2,6),(2,-6),(6,-2),(-6,2),(2,6)}
B. {(7,2),(-3,-5),(3,2),(6,7),(-3,4)}
C. {(-8,9),(8,-5),(-8,4),(6,-3),(8,1)}
D. {(-3,5),(6,10),(5,-2),(-6,-5),(3,9)}

Answer 1

D

Explanation:

In order for a line on a graph to be a function it has to pass the vertical line test.

How you do that for points, multiple X values can't have more than 1 Y value.

A has points (2, -6) and (2, 6), so it doesn't pass the vertical line test because the X value (2) goes to multiple Y values (6 and -6).

B has points (-3, -5) and (-3, -4), so it doesn't pass the vertical line test because the X value (-3) goes to multiple Y values (-3 and -4)

C has points (-8, 9) and (-8, 4), so it doesn't pass the vertical line test because the X value (-8) goes to multiple Y values (4 and 9).

C also has the points (8, -5) and (8, 1), and this has the same problem as all of the other problems.

D has {(-3, 5), (6, 10), (5, 2) , (-6, -5), and (3, 9)} which every X value has exactly 1 Y value.

Therefore, D is the correct answer.