A linear function is a function whose graph is a line in the plane. The characteristic property of these functions is that when the value of the input variable is changed, the change in the output is a constant multiple of the change in the input variable.
A linear function is a polynomial function in which the variable x has a degree, which is at most one.
The domain, which is the set of allowed values for x of a linear function, is the entire set of real numbers or whatever field that is in use. This means that any real number can be substituted for x.