Question

Select the correct answer. Which relation is a function? A. {(2, 3), (1, 5), (2, 7)} B. {(-1, 5), (-2, 6), (-3, 7)} C. {(11, 9), (11, 5), (9, 3)} D. {(3, 8), (0, 8), (3, -2)}

Answer 1

The answer is option B.

Explanation:

A rule that uniquely associates elements of one set A with the elements of another set B and each element in set A maps to only one element in set B.

Each element from X is related to only one element in Y. But it is okay for two different elements in X to be related to the same element in Y. So its still a function. Let suppose

{ (1,a) , (2, b) , (2, c) , (3, d) }

This relation is not a function from X to Y because the element 2 in X is related to two different elements, b and c.

Answer 2

Choice B represents a function

Explanation:

For a relation to be a function, each x input should yield exactly one y output. Going by this definition, the relation given by alternative A is not a function since the x input 2 yields two different values of y. For alternative C, 11 yields 9 and 5 as the outputs hence contradicting the definition of a function. For alternative D, the value 3 yields two different y values.