One can search for the functions in a library by searching the internet, e.g. https://sites.google.com/site/chrowe/cs50-cheat-sheet or http://www.techonthenet.com/c_language/standard_library_functions/stdio_h/ but how can this be done in the terminal itself, since this is faster.
if you want to "list the functions in a library", you should look at the header file(s) aka .h file(s).
if you wanna search for functions in the standard library, you could execute
man -f keyword
to search for man pages referenced by
man -k keyword
to search man page descriptions and names for
keyword as a regular expression.
man -f print
man -k print
man man to learn about more options for the