Transcription 1/14/2026, 10:44:03 AM

Notes

• Functions and Computing If you have already studied functions in mathematics, it is likely that what you were studying was a type of function known as a ‘real-valued function of a real variable’. If this is the case, then you probably think of a function as ‘something that has a mathematical formula,’ such as x² – 2x + 3, or ‘something you can draw the graph of’ using x and y axes. In computing (and in many areas of mathematics, for that matter), we take a different approach to functions, which turns out to be more useful. Our definition of a function is considerably more general, and in most cases, it will not be possible to draw graphs of the functions we will be studying. The way we think about functions will also be somewhat different. The functions used in programming in high-level languages (both the functions available in libraries associated with those languages and the function subprograms that you write yourself) are usually functions in this more general sense (with some qualifications, as we will see later). Functions of a real variable will be needed in Chapter 13 when we study the time complexity of algorithms. • Definition of a Function Let X and Y be sets. A f...