Topics:
• A review of the method for solving absolute value inequalities. (See at the end, below the fold, for a description of the method. We are not using the second method from the textbook, only the method used in Example 1.17.)
• Lines and slopes of lines
• Functions
• The domain and range of a function (Note: I will not be using the codomain)
• Examples of functions defined by a table, by a picture, or by a formula
• An example which is not a function
Homework:
• Routine homework problems: In Session 1, do the assigned problems in Exercise 1.7, especially if you have not done them yet! Make sure that you are carefully following all steps in the method described below.
• Do the assigned problems from Session 2, up to Exercise 2.6
• Read ahead: the rest of Session 2.
• Bring your graphing calculator next time!
• There is no Warm-Up this time. Also, the
WeBWorK assignment has been extended and is due on Sunday night 11 PM, as I posted the wrong assignment last time. Work on the Orientation assignment first! (If you have not yet logged in to WeBWorK, the instructions are in
this post.)
Solving absolute value inequalities
Method 1: See the three problems worked out in Example 1.17 in the textbook
First, solve the related equation. The solutions to the related equation divide the real line into several open intervals.
Next, choose a test point in each of those open interval (not the endpoints!) and check to see if it satisfies the original inequality. This determines whether or not each of the open intervals is part of the solution set.
Finally, check to see whether or not the endpoints of the intervals are in the solution set.
