Learning Resources
Outcomes
In this lesson you will learn
- a review of applying arithmetic operations to rational expressions
- to simplify complex fractions
By the end of this section students will be able to:
- describe the relationship between arithmetic operations and operations on rational algebraic expressions and equations
- determine the equations of polynomial and rational functions
- demonstrate an understanding for slope functions and their connection to differentiation
- analyze relations, functions, and their graphs
- use tables and graphs as tools to interpret expressions
- demonstrate an understanding for asymptotic behaviour
- model real-world phenomena using polynomial functions and rational functions
Introduction
In the previous sections of this chapter, you have worked with rational functions. In this section, however, you will learn to solve equations that contain rational expressions.
As well, you will deepen your understanding of rational functions as you analyze many to determine the zeros, asymptotes (horizontal, vertical and oblique) and any possible points of discontinuity. In addition, you will learn how to determine the intervals over which a rational function is positive or negative. All of these skills together will enable you to accurately graph rational functions.
This section requires about 6 hours for completion.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- factoring techniques
- fraction computational skills
- how to determine the domain of rational functions
- composition of functions (for questions 12 - 15)