Question

Which is a function and why?

{(1,-2), (1,2), (2,5), (2,-3)}
{(-2,1), (-1,0), (0,1), (1,2), (2,2)}

Answer 1

Step-by-step explanation:

A function is a relation (a set of ordered pairs) with the additional property that: no two pairs have the same first element and different second elements.

The definition is often stated as: A relation in which every

x

value is associated with exactly one

y

value. "Exactly one means one but two or more:

{(1,2);(2,3);(3,4);2,5)}

includes the points

(2,3) and (2,5)

. Therefore this set of pairse is not a function.

Note

{(0,1),(1,3),(2,5),(3,5)}

is a function.

(It is ok to have different first elements and the same second elements. The definition of function is very precise.)