Using null or not null in function arguments

I have a row search function, smth like

CREATE OR REPLACE FUNCTION user_func.search_users
(i_city_id int, i_edu_id int, i_first_name text, i_last_name text,
limit_ int, offset_ int) RETURNS SETOF user.user AS $$
..... SELECT * FROM user WHERE
city_id = i_city_id
...
$$ language plpgsql;

How do I write a function without complex logic, which will do:
a) If the input argument is NULL, then the corresponding select
statement will change from

column = arg
to
column IS NULL

maybe there is some built-in function for that?

b) If the input argument is NULL, then the corresponding select
statement will be removed, so if it was not written.

I think, this is a common problem.

Thanks in advance and regards,
Igor Katson.