Which produces a counter example to her statement

Question

Nancy made the following statement:

The range of f(x) = ax + b is the set of all real numbers given that a and b are real numbers.

Which produces a counter example to her statement?

Answer 1

 

 The range of f(x) = ax + b is the set of all real numbers given that a and b are real numbers.

The set of real numbers, R, is a subset of the complex numbers, C.

If we let x = i, then f(x)  is a complex number and is not within the real number set.