Domains and Ranges of Functions

Domains and Ranges: A Primer

There are a medley of functions that are NOT defined for all \(x\)-values. For instance, the function \(f(x)=\frac{1}{x(x-1)}\) is not defined at \(x=0\) nor at \(x=1\). For such functions, it is important that we know for which values the function IS defined.

In other words, the domain of a function is the set of all \(x\)-values that can be “plugged into” the function to get an output \(y\)-value.

The set of all \(x\)-values that are NOT in a function’s domain ought to be considered carefully, especially in Calculus-like settings.

Not only is it important to consider all possible inputs for a function, it is fruitful to know all of it’s possible outputs as well.

Think of range as the set of all possible \(y\)-values that a function can give you.

In the following topics, we concern ourselves with finding the domain and range of functions in each of the representations discussed so far.