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The rule for a set of ordered pairs is the statement that states the relationship of of a certain value to another value.For example:given the set of ordered pair { (1,2) , (3,4) , (5,6) , (7,8) }we notice that the value of y is increased by 1 as the value of x varies.For instance, in the first ordered pair which is (1,2) where 1 is x and 2 is y such that (x,y), 1 increased by 1. In other words, x is increased by 1.So we say that the rule of the ordered pair is:{(x,y) | y = x + 1 }read as "The set of ordered pairs such that y is equal to x plus one"
Removing one pair is not enough to make it a function. You need to remove one of the pairs starting with 1 as well as a pair starting with 2.
Although no incomplete ordered pairs have been shown they can be readily solved.If x + y - 1 = 0, then x = 1 - y, also y = 1 - x.From the above formulae for x and y then any omissions can be completed.EXAMPLE : complete the ordered pairs (1) (7, y) and (2) (x, -4)(1) y = 1 - x = 1 - 7 = -6 : The ordered pair is thus (7, -6)(2) x = 1 - y = 1 -(-4) = 5 : The ordered pair is thus (5, -4)
y=(-1) x=(2)