Let f(x) = Random Function
f() = As you trace out the graph, the red dots below trace out the Domain of the function, and the Blue dots to the right trace out the Range of the function.
You can also squash the graph onto the x-axis to find the domain or squash the graph onto the y-axis to find the range:
Squash onto x-axis (domain) Squash onto y-axis (range) Undo Squashing

Random Function with Nice Domain/Range