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The domain of a rational function is the whole of the real numbers except those points where the denominator of the rational function, simplified if possible, is zero.
If it's a linear function, 3 should do, but 4 will give an extra check on you work. If the function is quadratic exponential, etc. then at least 4 pairs should be used.
The answer depends on what group or field the function is defined on. In the complex plane, the range is the complex plane. If the domain is all real numbers and the radical is an odd root (cube root, fifth root etc), the range is the real numbers. Otherwise, it is the complex plane. If the domain is non-negative real numbers, the range is also the real numbers.
Discrete Function - A function that is defined only for a set of numbers that can be listed, such as the set of whole numbers or the set of integers. Explicit Definition - A definition of a function by a formula in terms of the variable.
the domain of the function