1. Heating: The primary function of a furnace is to provide heat for a building or space. They do this by burning fuel (like natural gas, propane, oil, or wood) to generate hot air or water, which is then circulated throughout the space.

2. Ventilation: Furnaces often incorporate a ventilation system to remove stale air from the building and bring in fresh air. This helps to improve air quality and reduce humidity levels.

It's important to note that while these are the two core functions, some furnaces might have additional features, like:

* Air filtration: Some furnaces come with built-in air filters to remove dust, allergens, and other pollutants from the air.

* Humidification: Some furnaces can also help to humidify the air during dry seasons.

* Cooling: Some systems combine a furnace with an air conditioner for year-round comfort.

So, the two fundamental functions of a furnace are heating and ventilation, with the possibility of additional features depending on the specific model and your needs.