Fiber Optic → [Questions/Help/Advice] how far does my docsis 3 modem have to transmit

FTTN (fiber to the node), backbone fiber network feeding 'last mile' nodes. also called hybrid fiber-coaxial plant

so i estimate my last mile connection is only a short copper run down the street and maybe around the corner

short copper runs like that aren't too bad. the fiber mains is just down the street

i forgot to add my main question:

i'm interested in these nodes, the ones that convert fiber backhaul to copper last mile runs

You forgot the actual question. What are you interested in with regards to these nodes?

i just want to learn how they work. i'd like to get a job working with them

So you'd like to become a technician? There are courses for that. Ask your local cable company or community college what they offer or recommend.

To learn the basics check out the wikipedia article on HFC. It cover the nodes as well.
»en.m.wikipedia.org/wiki/ ··· -coaxial

I might be able to offer a little input. Cable systems HFC network is essentially operating in a similar manner as radio when it hits the copper segments. So to trace it from your modem, that coax will eventually hit a distribution tap, which is wired into the hardline. The hardline will eventually hit either a node or an amplifier. If it hits an amp, the amp feeds into a node, and from the node it converts the signals to fiber.

Now the only actual equipment that actually does stuff on the copper end in an active manner are the amps and nodes. Taps and equalizers and other stuff act in more of a passive manner; you don't really configure anything on them. They can manipulate the signal but if they do, they are constructed to do this.

So from your modem to the demarc on your house to the tap, typically the run is going to be no more than 300 feet for RG-6 cable and 300 feet is really stretching it to the limit. Best practices will vary from each company but I'm sure they try to keep it less than that. They would probably use RG-11 for those distances, but even that has its own limits too.

The HFC system is interesting to me because it reminds me of the early days of ethernet networking. The whole system is a sort of bus and if you were to connect your PC straight to the modem, get signals sync'ed up, then turn on Wireshark, take a look at see what you get. If you are familiar at all with basic networking and the OSI model, do you know what layer this traffic falls under? Here's a good question: what layer of the OSI model do amps and taps operate on?

I might suggest you try and get a tech level ham radio license. It might seem odd, but you can learn a great deal from it and the study materials are free.

With modern DOCSIS 3.1 and DPoE standards, it's accurate to quote "as far as where fiber reaches near your home".
At your doorstep, on the poles outside your house or at the end of the street where you live.