(Includes after the test on Wednesday)
Topics:
- Sketching a complete graph of a polynomial
- Rational Functions and their graphs
- Solving polynomial inequalities using the same method we used to solve absolute value inequalities – see Section 1.4
A complete graph of a polynomial must show all of the important features of the graph:
- The x-intercepts (real roots) if any, and the y-intercept. Note that the y-intercept of a polynomial is the constant term.
- The turning points (local maxima or minima) of the graph, if there are any.
- The end behavior.
Here is the summary of graphing rational functions that I showed in class: it includes a worked example
Solving polynomial (and rational) inequalities:
We use the same method we have previously used to solve absolute value inequalities, that is:
First solve the corresponding equation
Then investigate the intervals to see if they solve the inequality or not
Then look at the endpoints
The only difference is that now we will make use of our knowledge of the graphs of polynomials (and later, rational functions) to investigate the intervals. This is equivalent to the “test point” method.
Homework:
• Review the examples discussed in class. Make especially sure that you understand how we are using the graphs to solve the polynomial inequalities in Ex. 12.2(a,b)
• Do the WeBWorK: the assignment on Polynomial Inequalities is not due until Tuesday, because it includes rational inequalities, which we have not yet discussed, but you can get started on the first few problems in the meantime.
• Also do the following problems from the textbook: Exercises 10.4(a-c and f-h), 11.4(all parts), and 12.2(a, c, d)
• No quiz next time.
Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!
