Mathematics 133 -- Intensive Calculus for Science 1
Plan for September 12, 13, and 14, 2001
How do you carry on after tragedies like those of the past few
days? As Fr. McFarland has said to the College community,
``There is little most of us can do in the short run to affect events
on the larger stage'', but ``it is important to [stay]
connected and involved, while providing the help and support everyone
needs.'' For this reason, I think it will be best if we meet at
the regular times, and try to move
forward with at least part of the mathematics that we had planned to
cover this week, while keeping some flexibility about assignments, etc.
- We will finish discussing the material on composition
of functions and inverse functions from section 1.3 on Wednesday.
- The problems from section 1.3 from the original Problem Set 2
will be due on Friday. The problems from section 1.4 (on logarithm
functions) will be postponed until next week. Extensions
on this assignment will be granted if you need them, though -- just ask.
- Also, you may resubmit solutions for problems from
the first problem set for additional credit.
- We will have our usual weekly problem session on
Thursday.
- A second quiz of the semester will be given
in class on Friday, September 14. Note:On Friday, even
if you feel as though you are unprepared for the quiz,
I would still recommend that you come and try to work on
the quiz problems during the 20 minutes to see the kind
of questions that will appear on exams later. We will discuss
the quiz questions following that, so you will see how to solve
them. Remember that only the highest
5 of your 8 quiz scores will be used in computing your final
quiz average, so this quiz will not hurt you in any case.
On the quiz, there will be two or three
questions similar to problems from section 1.3, but section 1.4 will
not be covered. You should know the following material.
- Obtaining new functions (and graphs) by
- Vertical shifts: y = f(x) + c (shifts up if c > 0
and down if c < 0)
- Horizontal shifts: y = f(x + c) (shifts left if c > 0
and right if c < 0)
- Vertical stretching or shrinking: y = cf(x)
(stretches if |c| > 1, shrinks if |c| < 1,
plus a ``flip'' across the x-axis if c < 0)
- Horizontal stretching or shrinking: y = f(cx)
(shrinks if |c| > 1, stretches if |c| < 1,
plus a ``flip'' across the y-axis if c < 0)
- compositions f(g(x)) and g(f(x))
- inverse functions, and the ``horizontal line test'' for
when a function has an inverse function
Good Review Problems:
- Chapter 1, section 3: 1,2,4,5,7,9,10,20,25,27,33