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

Answer: option D.

Step-by-step explanation:

A function is defined as a relation in which do no exist two values of y (output values) to  a same value of x (input value):

In option A the relation is $A. {(1, 1), (1, 2), (1, 3)}$. You can observe that for the same value x have three distinct values of y, therefore this is not a function.

In option B the relation is $B. {(1, 1), (2, 1), (3, 1)}$. You can observe that the values of x have sames values of y, but there are not two values of y for a same value of x. Then this relation is a function,

In option C the relation is $C. {(1, 1), (2, 2), (3, 3)}}$. You can observe that the values of x have distinct values of y, therefore this is  a function.  

Answer 2

Answer:

D. Both B and C.

Step-by-step explanation:

For an ordered pair relation to represent a function, then none of the first coordinate must repeat.

In other words, no two or more ordered pairs should have the same first coordinate.

For options A, the first coordinate repeated.

For options B and C, none of the first coordinates repeat.

Both represent a function.

The correct choice is D