Learning Resources
Outcomes
In this lesson you will learn
- what is meant by the term critical point
- how to determine the absolute maximum value of a function
- how to determine the absolute minimum value of a function
By the end of this section students will be able to:
- analyze relations, functions, and their graphs
- analyze the effect of parameter changes on the graphs of functions and express the changes using transformations
Introduction
Many of the topics studied thus far in the chapter may seem disjointed to you. This section attempts to bring together, in a meaningful way, all of these concepts.
Throughout this course you have been encouraged to keep a Function Toolkit Notebook to summarize the skills used to work with polynomial functions and the basic shapes of polynomial functions you have discovered and used. You have also been exposed to the ways in which the sketches of polynomial functions can be completed. In this section a more formal approach is used to summarize these methods so that, in the final analysis, you will be able to sketch any polynomial function. You will have the necessary skills to deal with polynomial functions with comfort and ease and, as a result, have a firm foundation for future calculus studies.
It should take approximately 2 hours to complete this section of study.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- how to find the x and y-intercepts of a function
- slopes of tangents
- increasing and decreasing functions
- maximum and minimum values of a function
- domain and range