Question 1198361: Which of the following is a function?
A) [(1,2),(3,2),(1,3)]
B) [(1,3),(2,3),(6,7)]
C) [(9,4),(2,1),(9,6)]
D) [(6,2),(8,3),(6,4)]
E) [(2,6),(2,7),(2,9)]
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Choice A is not a function because the input x = 1 has multiple outputs (y = 2 and y = 3 at the same time).
A function is only possible if any given x input leads to exactly one y output.
Choices C, D, and E are also not functions for this similar reasoning.
Choice B on the other hand is a function.
None of the x coordinates repeat themselves. Each item is listed exactly once.
The y values can repeat, but the function wouldn't be one-to-one.
A visual alternative tool is to use the vertical line test.
If it is possible to draw a vertical line through more than one point, then that relation is not a function.
In such a case, it is said this relation fails the vertical line test.
This is what it looks like for the points from choice A
The points (1,2) and (1,3) make this relation fail the vertical line test. I'll let you form the graphs of the other answer choices.
--------------------------------------------
Answer: Choice B
|
|
|
