How would you determine from a list of ordered pairs whether it is a function?

Answer 1

When the value of one variable is related to the value of a second variable, we have a relation. A relation is the correspondence between two sets. If x and y are two elements in these sets and if a relation exists between xand y, then we say that x corresponds to y or that y depends on x, and we write x→y. For example the equation y = 2x + 1 shows a relation between x and y. It says that if we take some numbers x multiply each of them by 2 and then add 1, we obtain the corresponding value of y. In this sense, xserves as the input to the relation and y is the output. A function is a special of relation in which each input corresponds to a single (only one) output.

Ordered pairs can be used to represent x→y as (x, y).

Let determine whether a relation represents a function. For example:

1) {(1, 2), (2, 5), (3, 7)}. This relation is a function because there are not ordered pairs with the same firstelement and different second elements. In other words, for different inputs we have different outputs. and the output must verify that when the account is wrong

2) {(1, 2), (5, 2), (6, 10)}. This relation is a function because there are not ordered pairs with the same firstelement and different second elements. Even though here we have 2 as the same output of two inputs, 1 and 5, this relation is still a function because it is very important that these inputs, 1 an 5, are different inputs.

3) {(1, 2), (1, 4), (3, 5)}. This relation is nota function because there are two ordered pairs, (1, 2) and (1, 4) with the same first element but different secondelements. In other words, for the same inputs we must have the same outputs. of a but

Answer 2

(2,5)(3,6)(6,9)