Chapter 3 : Graphing and Functions
Here are a set of assignment problems for the Graphing and Functions chapter of the Algebra notes. Please note that these problems do not have any solutions available. These are intended mostly for instructors who might want a set of problems to assign for turning in. Having solutions available (or even just final answers) would defeat the purpose the problems.
If you are looking for some practice problems (with solutions available) please check out the Practice Problems. There you will find a set of problems that should give you quite a bit practice.
Here is a list of all the sections for which assignment problems have been written as well as a brief description of the material covered in the notes for that particular section.
Graphing – In this section we will introduce the Cartesian (or Rectangular) coordinate system. We will define/introduce ordered pairs, coordinates, quadrants, and x and y-intercepts. We will illustrate these concepts with a quick example.
Lines – In this section we will discuss graphing lines. We will introduce the concept of slope and discuss how to find it from two points on the line. In addition, we will introduce the standard form of the line as well as the point-slope form and slope-intercept form of the line. We will finish off the section with a discussion on parallel and perpendicular lines.
Circles – In this section we discuss graphing circles. We introduce the standard form of the circle and show how to use completing the square to put an equation of a circle into standard form.
The Definition of a Function – In this section we will formally define relations and functions. We also give a “working definition” of a function to help understand just what a function is. We introduce function notation and work several examples illustrating how it works. We also define the domain and range of a function. In addition, we introduce piecewise functions in this section.
Graphing Functions – In this section we discuss graphing functions including several examples of graphing piecewise functions.
Combining functions – In this section we will discuss how to add, subtract, multiply and divide functions. In addition, we introduce the concept of function composition.
Inverse Functions – In this section we define one-to-one and inverse functions. We also discuss a process we can use to find an inverse function and verify that the function we get from this process is, in fact, an inverse function.