Does the map() function works on an ATtiny85?
The map function uses integer arithmetic, and since the ATmega series and the ATtiny series use the same 8-bit AVR instruction set, there should be no difference when using it, and you are good to go from that aspect.

Consider that there are many other differences regarding I/O pins, storage etc. - that you might want to consider. Here is a good source for a basic comparison between the ATmega based Arduino to ATtiny85.