Topics:
• A second method for solving absolute value inequalities (See update below)
• 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, by a description (the greatest integer function), or by a formula
• An example which is not a function
Homework:
• Routine homework problems: In Session 1, do #1.7(e) (and the rest of the assigned problems if you have not done them yet! Try using both methods.
* Do the assigned problems from Session 2
• in Session 3 do #3.6 only
• Read ahead: the rest of Session 3.
• 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.)
• The first day’s Warm-Up is still open, until Wednesday evening only!!! Please make sure that you do it so you can be invited to join the online discussion group.
UPDATE: See below the fold for descriptions of the two methods for solving absolute value equations. Make sure that you are following a correct method!
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.
Method 2: You translate the absolute value inequality into a form that does not have absolute value signs in it and then solve the resulting inequalities.
In the following, c is a positive real number.
|something| < c
translates to the double inequality
-c < something < c
You solve the double inequality by performing the same operations on all three parts until x is isolated in the middle. See Example 1.18 in the textbook.
|something| > c
translates to
something < -c or something > c
You solve the two inequalities separately. The solution set has two pieces. See Example 1.19 in the textbook.
