Professor

Hello, my name is professor Feras Ahmed, and today I’m going to teach how find a domain of a function and the domain and range of a relation. What is the domain? The domain, we often hear it combined with domain and range, but the domain of a function is just what a value can I put into a function and get a valid output. For example; f (x)=x^2, what value of X I can use to get a valid answer for X squared. I can use any real number so I can say Domain is the set of Xs such as X is a member of the real numbers, Domain = {X Î IR}.

Examples: f (x) = 1/x^2

f (0) = 1/0  what is 1/0??  

 This is undefined because we can’t put zero instead of X and get a valid number (output) and f (0) is undefined as well. In this case we say the domain is {X Î IR: x¹ 0} X is a member of a real number except zero. In the first example X is a real number, but in the second example X is areal number except zero. 

Domain and Range of a Relation;

Determine the domain and range for the relation described by the table.

X	Y
6	-1
4	8
3	2

When we say the domain we mean what are all the possible inputs that we can put into the relation. What are all the inputs that this relationship is define for? We can view X as the input, so when X is 6 Y is -1 and so on.

Domain = {6,4,3}, so all we are saying here that this relationship is defined for any of these numbers, so if I give any of these numbers as an X value, there’s a Y value associated with it.  Now when we talk about the range of this relation and the idea also applies to functions, the range is what are all the possible output that this relation can give you or giving the inputs what are all the possible values (outputs).

Range = {-1,8,2}   

That was our lecture for today, don't forget to do the exit-slip before you leave :)

Have a good weekend