Question

what are the domain and range of the function relating the pressure and volume of an ideal gas at a constant temperature, as given by Boyle's law?

Answer 1

Boyle's law says that we can write the relation PV as:

P*V = k

where P is pressure, V is volume and k is a constant.

Then we can have the function P(V) = k/V.

As V is the denominator, as V increases, the pressure decreases.

Now, the only restriction we have for the volume is that it can never be zero.

V > 0.

So the domain is V ∈( 0, inf)

Now, when V is near zero, the pressure tends to infinity, and when the volume is big enough, the pressure tends to zero (but it is never zero actually)

So the range of the function is P ∈( 0, inf)