Is it possible to visualize a bunch of functions in UML

There is no UML element for representing independent functions.

You may however consider a free standing function as a special form of object in its own class. In fact, in some designs, “functor” objects are even designed to be used in place of a functions.

To avoid possible confusion, you may extend the class diagram with your own profile that would define a stereotype «function». Stereotypes are supported by any serious UML modeling tools (here for visual paradigm).

The multiplication of such micro-classes might not necessarily make your documentation easier to understand. You may therefore consider to regroup closely related functions in the same “box” (stereotype «function group» or «module» ?). Your narrative suggests for example that you have a group of functions which implement in reality a repository (from the list you gave: adding, changing, deleting, searching the same kind of persistent objects) or a view (from your explanation about visualization): the grouping would then in any case facilitate to understand their close relationship.

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