Posted by Sam R. on Friday, June 25, 2010 at 4:11pm.
The answer to the question lies in the definition of a function, which is a transformation from a set X of values to a set Y of values, such that any value in the set X will be transformed to one and only one value in the set Y.
An ordered pair (x,y) represents one particular element x in the set X that will be transformed into an element y in the set Y.
The formal notation is
y = f(x), where x∈X and y ∈Y.
The set X is called the domain, and contains all valid values of x. The set Y is called the range, and contains all possible values of y.
An example of a function is
y = f(x) = x², and some ordered pairs are: (-1,1), (0,0), (1,1), (2,4), (3,9).
Note that even though some values of y have been duplicated, the same value of x always give one and only one value of y.
If we had a relation such as
y = sqrt(x),
we would have ordered pairs such as
(0,0), (1,1), (1,-1), (4,2), (4,-2).
In this case, since y=±sqrt(x), the same value of x is not transformed to one single value of y, and so sqrt(x) is NOT a function.
Take it from here and post your answer for a check if you wish.
the domain is all of ur x values and the range is ur y values
a set of ordered pairs is a function if it passes the vertical line test, which means you can draw a vertical line anywhere on the line and it wont cross two points. the way a set would be a function is if all of the x values are different
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