Monday

June 27, 2016
Posted by **Sam R. ** on Friday, June 25, 2010 at 4:11pm.

What is the difference between domain and range? Provide an example of at least five ordered pairs that do not model a function. The domain will be any five integers between 0 and 20. The range will be any five integers between -10 and 10. Your example must not be the same as those of other students or the textbook. Why does your example not model a function?

- functions -
**MathMate**, Friday, June 25, 2010 at 7:13pmThe 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. - Algebra 1 -
**A**, Monday, June 28, 2010 at 3:38pmthe 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