Topics:
• More on functions defined by formulas:
Difference quotients (Example 3.3)
Finding domains of the four types of functions we have studied so far (Example 3.5)
I strongly recommend computing the difference quotients by breaking the process down into 3 steps, as I did in class (and as is done in our textbook):
First, find
Then find
Finally, find
Write down what it is that you are computing at each step, as I did (and as they do in the textbook) – this makes it easier to follow when you or someone else goes back to read your work.
When finding the domains of the four types of functions, it is important that you understand why we do what we do.
For a polynomial function, there is no problem substituting any real number into its formula, so the domain is the set of all real numbers 
For a radical function of even index like a square root function, the radicand cannot be negative, because for the time being we are insisting that the values of the function must be real numbers. So we need the radicand to be 
IMPORTANT: solve that inequality to find the domain. DO NOT SOLVE AN EQUATION AND THEN STICK AN INEQUALITY SIGN INTO THE RESULT! That will not always work, and you may forget the inequality sign!
For a rational function, we need the denominator not to be 0.
For a piecewise-defined function, the domain is the union of the pieces of domain where it is defined. Sometimes (not always) that union can be simplified.
Study the examples I discussed in class and make sure that you understand why we do what we do!
• New topic: lines and their slopes, and putting the equation of a line into slope-intercept form 
It is most important that you develop an intuition for how the slopes affect the graphs. See the graphs with different slopes which are given on p. 15 in Section 2.1.
Homework:
• Last reminder: make sure that you have done everything that is listed on the first day post! Most especially, make sure that your City Tech email address is in the User Information in WeBWorK. There are still a number of student who have not done this, and it means that if you send me an email from inside of WeBWorK I will not be able to reply to your email.
• Review and study the examples we discussed in class (listed above). You may also want to refer to my slideshow MAT1375-FunctionsByFormulas-slideshow which I used last time.
• Do the WeBWorK: due by 11 PM tomorrow, Tuesday, and please do not wait to the last minute!
• Also do the following from the textbook: Exercises 3.1 (a)-(b), 3.2, 3.4 (a)-(f), 3.6 (a)-(h)
These contain extra practice and also a few things that are not in the WeBWorK.
• Make sure that you bring your graphing calculator to class next time and every time from now on, so you get practice in using it. We will use it extensively next time.
• Tomorrow is primary election day in NY, so if you are a registered voter check out the NYC Campaign Finance Board’s Voter Guide and don’t forget to vote!
I believe that I have corrected or fixed all of the links in the previous posts on this blog, but if you find a link in any post that is broken or leads to the wrong thing, please let me know!
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!
Here is my slideshow on how to use Piazza to best effect: MAT1375:1575-UsingPiazza-slideshow
