Lecture 16:

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Problem of the day

This problem is due on Friday, March 5:
POW 8

Assignments during second test period.

These are the problems you should work before March 5.

Section 2.2 page 205 problems 8n+1, for n=0,...,11;

Section 2.3 page 218 problems 1-6 and 6n+1, for n=1,...,8;

Section 2.4 page 232 problems 1-6 and 4n+1, for n=2,…,22;

These are the problems you should work before March 19.

Section 2.5 page 244 problems 1-6 and 6n+1, for n=1,...,14;

Review page 249 problems 4n+1, n=0,…,14;

Section 3.1 page 263 problems 1-6 and 4n+1, for n=0,…,19;

These are the problems you should work before March 26.

Section 3.2 page 277 problems 4n+1, n=0,...,12;

Section 3.3 page 289 problems 4n+1, n=0,...,7;

Section 3.4 page 298 problems 4n+1, n=2,...,7

 Deadlines for submitting the ICA tutorial software post-tests:
The policy for late submission is that the student loses 5 points per week for each posttest which is submitted late. The loss begins the day following the deadline.

Accessing the software tutorial for this course

The software package Interactive College Algebra is now available for your use. As an introductory offer, I will give up to 25 extra points for your first use of this package. These points will offset low quiz scores and low POD scores, each of which counts 5 points. To access the software you must either install it on your home or dorm computer or visit the lab Fretwell 321. This is the only place on campus which has it installed. To get extra points, there is a two step process. First, you must access it and complete one of the Chapter Post-tests for chapters 2 or 3. These are randomly generated multiple choice problems. The second step is to email to me the testlog.txt file generated by your use of the package.

Here's how to do the first step: a. use the START key in the lower left corner.
b. go to programs, then Int. College Algebra, then Interactive College Algebra.
c. then go to Chapter 3.
d. Then click on study aids for this Chapter, and finally on Chapter Post-test.
e. Click on BEGIN TEST. When you complete a question, move to the next question by clicking Next Question. The deadline for earning extra points by doing the Chapter 2 posttest is October 15. The deadline for earning extra points by doing the Chapter 3 posttest is October 22. The deadline for earning extra points by doing the Chapter 4 posttest is November 22. You'll get one point for each problem you work correctly on the first try. When you finish, a testlog file will be automatically produced. You can earn extra points twice. To earn extra points twice, you must do two different chapter tests.

Step two of the process is to email to me the logfile your computer generated. The best way to do this is to attach the file to the message. Ask the attendent about attaching files to email messages if you have not done that before. Be sure to include your name on the message. The file is located on the c: drive in the directory \ica.

Brief review of the lecture

The single most important operation on functions is composition of functions. There are many ways to form new functions out of old ones, like adding them, multiplying them, or subtracting them. These are operations we can perform on all real numbers, so we can easily understand these operations. But composition of functions is an operation that we can only perform on functions. You'll see in the calculus course a formula called the Chain Rule. Its purpose is to enable you to find the derivative of a function which is build as a composition. In order to understand the use of this important rule, you must understand composition of functions very well. For that reason, we'll spend more than one full lecture discussing this operation. We looked at two functions, g(x)=2x, the doubling function, and f(x)= x^2, the squaring function. We found both compositions fog and gof. Then we considered other examples.

Leftovers

The idea of a function was introduced today. This concept is arguably one of the most important ideas in mathematics. It is one that you are expected to understand. If you miss any lecture on functions be sure that you get notes from a classmate. Also, you must read section 3.1 and 3.2 of the text carefully.

Functions can be defined and represented in various ways. You are expected to understand the connections between the various representations of functions.

Functions can be represented by

a graph

a table of values

an equation (the most common in this class)

a set of ordered pairs.

Two definitions of function:

  1. A function f is a rule which associates with each element of a set A exactly one element of a set B.
  2. A function: A -- B is a relation whose ordered pairs have first coordinates taken from A and second coordinates taken from B, and
    1. Every member of A is a first coordinate of some ordered pair
    2. No two ordered pairs have the same first coordinate.

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