Learning Resources
Outcomes
In this lesson you will learn
- the definition of a rational function
- how to tell if a function is continuous or discontinuous
By the end of this section students will be able to:
- describe the relationships between arithmetic operations and operations on rational algebraic expressions and equations
- analyze relations, functions, and their graphs
- use tables and graphs as tools to interpret expressions
- demonstrate an understanding for asymptotic behaviour
- analyze and solve polynomial, rational, irrational, absolute value, and trigonometric equations
- explore and describe the connections between continuity, limits and functions
- demonstrate an intuitive understanding of the concept of limit
Introduction
Thus far, your study of rational functions has been limited to only those in which the numerator is a constant. This section serves to extend your understanding of rational functions to include ones in which the numerator is a polynomial expression. The method in which you attain this new knowledge will be the same as in the previous section. You will first sketch the graphs of several rational functions and then use them to help you predict the locations of vertical, horizontal and oblique asymptotes. In addition, you will discover the behaviour of the functions about these asymptotes and learn to recognize points of discontinuity.
This section of study takes approximately 4 hours to complete.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- left and right hand limits
- the concepts of a vertical asymptote
- an understanding of how the graphs of previously studied reciprocal functions behaved asymptotically for certain values of x