Lesson 5A: Exploring Polynomial Functions

The notion of function is one of the most important ideas in mathematics. Functions are the basis of mathematical applications in many fields including financial management, computer programming, and engineering. Because functions are so widely used, knowing their characteristics is useful so you can recognize them in the world around you.

Informally, a function is a rule that assigns a unique element y to each element x in a set of data. In other words, for each value of x, the independent variable, there is precisely one corresponding value of y, the dependent variable.

Functions can be expressed in four ways: equations, graphs, tables, or words. This lesson focuses only on equations and graphs.

On a graph, the set of data that represents a function can produce a wide variety of patterns. In previous math courses, you have seen the simplest patterns: linear and quadratic.

This lesson introduces the more complex cubic pattern.

In Lesson 5B, you will graph data and construct an equation to model the data. To do this, you must first review the basic characteristics of functions and understand how they relate to the graph and equation.

In this Training Camp, you will extend your prior knowledge of linear and quadratic functions. You will use this knowledge to investigate cubic functions and to study their characteristics.

By the end of this lesson, you should be able to

	describe characteristics of a polynomial function by analyzing its graph
	describe characteristics of a polynomial function by analyzing its equation
	match the equation of a polynomial function to its corresponding graph