Does it cost more for gas if you continually turn the thermostat off and then back on when you come and go into the home as opposed to keeping the thermostat at say 50 degrees so it does not kick on. This would pertain to when it is cold outside and also for when it is warmer outside (above 50 degrees say). A service technician said it's cheaper to keep turning it on and then off, etc. but the gas bills are quite high.

How about using a setback thermostat... you can program it for one temprature when you are away... as well as a lower one when you sleep.. but a warmer one while you are in the house.
But what is cheaper or not is determined by how long you are away from the house every day... and assuming its one long period and not several short periods.

It requires less total energy to not run the furnace at all when away and then turn it on again when you get home. It's simple heat flow theory - enegy usage is proportional to the rate of heat loss through the walls which in turn is proportional tp difference in temp between inside and outside. However, depending how cold it is outside and how long you're away you may find that it takes a long time for the house to heat up to a comfortable temp after you turn it back on, so what I do is not turn it off commpletely when I' away but rather set it back to around 60 degrees if I'm going to be gone just for the day (say to work) and to around 55 if I'm going to be away for more than a day. I am also concerned about frozen pipes - if it gets much below 55 near the thermostat in my house then there are certain pipes in outside walls that may get close to freezing.