Any time a function is given by some formula, we say that the function is algebraic. A familiar formula from chemistry is PV = kT, where k is a constant, P the pressure, V the volume, and T the temperature of an ideal gas. Thus, T = PV/k is an algebraic function to determine the temperature based on the pressure and volume. We could write this as T(P,V) = PV/k. This type of function is most common in mathematics and physics.
To evaluate an algebraic function, simply use the formula. For example, if z = f(x,y) is given by f(x,y) = 3xy + 2y2 then x = 3, y = -1 yields z =3(3)(-1) + 2(-1)2 = -7.