You need to check if any logic is placed in a subscription that can block call of this function. If there is - it may be worth to extract it to a parameter (eg. filter) so that logic can be a part of stream itself.
I assume that observable (source) is injected/redirected from another component (if it's not, most probably it should be). To mock that signal you can use TestableObservable
, you can read more here: http://adamborek.com/rxtests-rxactionsheet/
Last but not least - you need to identify what kind of action somePrivateFunction()
does. If it's setting some external values - then you can test that outgoing connection from that function. If it sets some internal flags - you can test if value of that flag has changed.