Question

Which of the following relations represents a function?


A. {(1, 1), (1, 2), (1, 3)}
B. {(1, 1), (2, 1), (3, 1)}
C. {(1, 1), (2, 2), (3, 3)}
D. Both B and C

Answer 1

With functions, you can't have the same input (left value in an ordered pair) with multiple outputs. However, it is OK for multiple inputs to have the same output.

Think about it like a function where you input someone's name, and the output is the score they got on their last test. It makes sense for 2 inputs (i.e. Alice and John) to have the same output (i.e. 92%) But it wouldn't make sense for the same input to have more than one output. (i.e. Alice can't have 83% and 92% at the same time)

With that in mind, A obviously isn't a function because it has multiple outputs for the input value 1, but the other two do represent functions.

Answer 2

i stiil dont' get it

Answer 3

The numbers in the parentheses are called ordered pairs. If the ordered pair is (a,b) a is the input value and b is the output value. For every value a that you can put in, there is only one value b that you can get out. The thing you need to look for in this sort of problem problem is a group of ordered pairs with the same input value and different output values.

{(1,1),(1,2),(1,3)} has three ordered pairs with the input value of 1, but they all have different output values. That means it can't be a function.