A good place to start might be to consider the definitions. What is the definition of domain? What does it mean that a function's domain is all real numbers? What is the definition of range? What does it mean that the range is the set containing the elements 1, 2, and 3? Note that the range does not contain any values between 1 and 2, nor any values between 2 and 3, only exactly those integer values. What does that tell you about the function? Finally, I'd note that there's not one unique solution to this problem. There are infinitely many functions which have the given domain and range. The problem statement really should have asked you to graph "a function" with that domain and range, not "the function" (although that's not really your fault, that's the problem of the person who wrote the exercise)
