Addition and subtraction of linear functions Relations between functions and their sum Below are three examples of a pair of functions and their sum. In each example a decreasing function is added to an increasing function, but the properties of the resulting sum function are different: in one case it is increasing, in another decreasing, and in the third it is constant. In your opinion, which of the properties of the summed functions determine the properties of the sum function? You may want to begin by answering a few more focused questions first. For example: Is it possible to add two increasing functions and obtain a decreasing function? When will a constant function result by adding functions that are not constant? Use the Finding a function with a given sum tool to select a type of sum function (increasing, decreasing, or constant). Then find two functions whose sum is the function displayed. Report on the relations between the properties of the functions that are added and the properties of the sum function.

Addition of linear functions Subtraction of linear functions Relations between functions and their sum Properties of the difference graph Constructing a difference graph Shared savings Publishing a book Connection to the Internet Car chase Hot and cold drinks Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5