# Special Graphs

### Introduction and Summary

This chapter continues to explore the graphs of functions. It explores symmetry across a line and around a point, as well as asymptotes and holes. Using asymptotes and holes, this chapter also explains how to graph functions containing rational expressions. In addition, it focuses on the graphs of two specific functions: the absolute value function and the cubic function.

The first section deals with three types of symmetry--symmetry with respect to the x -axis, symmetry with respect to the y -axis, and symmetry with respect to the origin. It also explains the more general concept of an axis of symmetry. This section explains how to determine whether a graph has a given type of symmetry.

The next section is about asymptotes and holes. An asymptote is a line that a graph approaches without touching, and hole is a single point at which a function has no value. This section will explain why asymptotes and holes exist on graphs.

Since asymptotes and holes are an important part of graphing rational functions, the next section focuses on graphing these functions. Here, the steps for graphing rational functions are outlined.

The final section deals with two specific functions: the absolute value function and the cubic function. This section explains how to graph the absolute value function f (x) = | x| and the cubic function f (x) = x 3 , and explores transformations of both graphs.

The primary focus of this chapter is functions and their graphs. It explores the effects of certain properties of functions on their graphs. This serves a dual purpose--it helps us understand, given an equation, what the graph of the function looks like, and it helps us understand, given a graph, what the equation of the function looks like. Both of these skills will become especially useful in calculus.

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