Math 106 Fall
2011 

Function
vs. Process 

FUNCTION TYPES 
CONCEPTUAL UNDERSTANDINGS (PROCESSES) 
A. Polynomial (alinear, bquadratic, ccubic, and dhigher degree forms) 
1. Solving: solving equations, finding zeros, taking inverses (Use reverse Order of Operations) 
B. Rational 
2. Evaluating:
evaluating fun 
C. Piecewise 
3.
Recognizing chara 
D. Exponential 
4. Translating
from the symbolic to the graphic representation of a fun 
E. Logarithmic 
5. Translating
from the graphic to the symbolic representation of a fun 

6. Finding domain and range 

7. Finding
the inverse of a composite or combined fun 

8. Combining
Fun 

9. Modeling 
For each function type (Aa through E) listed, be able to demonstrate each of the processes (1 through 9) listed.
A Four Step
Problem Solving Process*:
While every problem is
different, the process of problem solving can share common features. The
following fourstep process provides a useful guide to problem solving. Keep in mind that these four steps offer general
advice and do not automatically lead to a solution. This method is offered as a good starting
point that is, a way to proceed if you are unsure as to what you should do
first.
STEP I: Understand the Problem. Be sure that you understand the nature of
the
problem. For example:
·
Think about the
context of the problem (that is, how it relates to other problems in the real
world) to gain insight into its purpose.
·
Make a list or
table of the specific information given in the problem, including units for
numerical data.
·
Draw a picture or
diagram to help you make sense of the problem.
·
Restate the
problem in different ways to clarify its question.
·
Make a mental or
written model of the solution, into which you can insert details as you work
through the problem.
·
Make sure you
understand ALL of the terminology used and how the context affects the facts.
Step
II: Devise a strategy for solving the
problem. Finding an appropriate
strategy requires
creativity, organization, and experience.
In seeking a strategy, try any or all of the following (as well as
others you may think of):
·
Obtain needed
information that is not provided in the problem statement, using recall,
estimation or research.
·
Make a list of
possible strategies and hints that will help you select your overall strategy.
·
Map out your
strategy with a flow chart or diagram.
·
Recall the
formulas or strategies with which you are already familiar and think about how
they might relate to the current situation.
·
Recall if you
have solved a similarly stated problem in the past.
Step III: Carry out your strategy, and revise it if
necessary. In this step you
are likely to
use analytical and computational tools.
As you work through the mathematical details of the problem, be sure to
do the following:
·
Keep an
organized, neat, and written record of your work, which will be helpful if you
later need to review your solution.
·
Double each step
so that you do not risk carrying or minus sign errors through to the end of
your solution.
·
Constantly
reevaluate your strategy as you work. If
you find a flaw in your strategy, return to Step II and create a revised
strategy.
Step
IV: Look back to check, interpret, and
explain your result. Although you
may be tempted
to think you have finished after you find a result in Step III, this final step
is the most important. After all, a
result is useless if it is wrong or misinterpreted or cannot be explained to
others. Always do the following:
·
Be sure that your
result makes sense. For example, be sure
that it has the expected units, that its numerical value is sensible, and that
it is a reasonable answer to the original problem.
·
Once you are sure
that your result is reasonable, recheck your calculations or find an
independent way of checking the result.
·
Identify and
understand potential sources of uncertainty in your result.
·
Write your
solution clearly and concisely, including discussion of any relevant
uncertainties or assumptions.
· Consider and discuss any pertinent implications of your result.