What are a function’s meaning, definition, and range?

"Now as with relations, functions normally have “meaning.” We could define a function called “firstTasted” that associates each wizard with the soft drink he or she first sampled as a child. We could define another called “faveDrink” that maps each wizard to his or her favorite, presuming that every wizard has a favorite drink in the set. A third function called “wouldChooseWithMexicanFood” provides information about which drink each wizard provides with that type of cuisine. Here are Ron’s values for each of the three functions: firstTasted(Ron) = Mt. Dew; faveDrink(Ron) = Mt. Dew; wouldChooseWithMexicanFood(Ron) = Dr. Pepper. These values indicate that Mt. Dew was the soda pop that Ron first sipped, and it has been his favorite ever since, although at La Estrellita he prefers a Pepper. Functions can be defined intensionally or extensionally, just as with relations. Intensionally, we provide the conceptual meaning of what the function represents. Extensionally, we list the values for each element of the domain. One other term that applies to every function is its range. A function’s range is the subset of the codomain that at least one element of the domain actually maps to. It’s the part of the codomain that’s “reachable.” For instance, if the function G : X → Y is { (Harry, Dr. Pepper), (Ron, Dr. Pepper), (Hermione, Dr. Pepper) }, then even though the codomain is { Dr. Pepper, Mt. Dew } the range is merely { Dr. Pepper }. That’s because there isn’t any ordered pair that contains Mt. Dew, so it’s left out of the range. You can’t “reach” Mt. Dew via the G function by starting with any of its inputs, so it’s left out in the cold. By the way, a function’s range is sometimes called its image. These terms are synonymous."