Is it possible to send a fax without owning a fax machine?

Yes. If you do a search for "how to fax without a fax machine" a number of option will turn up. Since I haven't performed this operation myself I can't tell you how it works or how complicated it might be.

There are many places that will send your fax for a low fee like office max and staples, but there is an app that you download and you can send a fax from your iphone for free.

I have used Staples, so good advice.