COALITION MATH 151, FALL 1997

        Group II (S. A. Fulling, assisted by Cary Lasher)

                             Day 2.1


    1.  Questions?  Collect homework.

    2.  RAT

        A.  Individual part:  Explain in your own words what a 
        function is.  (The number of sentences on your paper 
        should be an integer greater than 0.)  (2 minutes)

        B.  Team part:  Arrive at a team answer to the question and 
        e-mail it to the grader.  (3 minutes)

        C.  Grading:  Team response will be graded.  Individual 
        responses will be read by the professor.
SOME ESSAYS WERE GOOD, BUT OVERALL THE RESULTS WERE SOMEWHAT 
DISAPPOINTING.  MANY STARTED OUT SOMETHING LIKE "A FUNCTION IS AN 
EQUATION ..."   THE VERTICAL LINE TEST DOES SEEM TO BE 
UNDERSTOOD.

        D.  My RAT philosophy:  The best use of class time is for 
        interaction, so I dislike written individual RATS.  
        However, they will occasionally happen, to keep you on 
        task (especially if attendance falls off on Fridays).

    3.  Mention shifting and scaling (show slide, along with 
    graphs of elementary functions).  This will be the subject of 
    a drill tomorrow. 
        
    4.  Composition of functions (random individual response; 
    team gets 2 points if individual answers, 1 point if teammate 
    answers). 
MY EXAMPLE TURNED OUT TO BE FLAWED.  THIS IS AN IMPROVEMENT:

        A.  Let y = f(x) = x^2 + 1,
                z = g(y) = sqrt(y),
                w = h(z) = sin z - 1.

        B.  z = g o f(x) = g(f(x));   w = h o g(y)

        C.  What are the domains of these two functions?

        D.  (h o g) o f;   h o (g o f)

        E.  Conjecture a theorem on the basis of C.
RAN OUT OF TIME HERE (MOSTLY BECAUSE PASSING OUT CAPA SHEETS WAS 
TIME-CONSUMING).  COMPLETED NEXT TIME.  STUDENT RESPONSES ON 
THESE QUESTIONS WERE ALL CORRECT ON THE FIRST TRY, EXCEPT FOR THE 
"FUNCTION" WITH NULL DOMAIN (g o h in the revision), WHICH CAUSED 
SOME CONFUSION. 

        F.  [rename the variables as necessary]
            f o g;   f o h;   h o f;   g o h;

        G.  What are the domains of these 4 functions?