A linear relationship between two variables occurs when there is a constant increase or constant decrease in one variable with respect to the other. Linear functions have the property that any chance in the independent variable results in a proportional change in the dependent variable. Many physical situations can be modeled using a linear relationship. Adding an extra term of the form ax^2 to a linear function creates a quadratic function, and its graph is the parabola. We will see examples of linear and quadratic functions and their applications in the sections that follow.

In the last module we introduced the important concept of a function and considered the linear and quadratic functions. In this module, we discuss methods for building new functions from those that are already familiar to use. One method will use the graph shifting techniques already introduced. These methods are developed further and applied to new functions. Constructing a graph is often an important first step in solving a problem. The more functions you can picture, the better problem solver you will be.

Congratulations on reaching the final exam! This final assessment will be cumulative in nature, covering all aspects of the course. Use this final as a teaching tool: justify what you know and identify areas for improvement. Use scrap paper as you take this final. Try to use any formula sheets or outside resources as a tool and not a crutch. Check your answers before you submit. After the test, review any incorrect answers to find your mistakes. Try to separate "silly" mistakes from the more substantial mistakes in understanding. Good luck!