COLLEGE ALGEBRA
These brief notes are intended to guide you through the textbook and/or other course readings/materials. As you read the textbook pay particular attention to the "topics of importance" and be sure you know how to accomplish each. The "supplemental sites" may provide additional resources on the internet that supplement the topics. Note: This material is extensively elaborated upon in my optional e-book GOLDen Mathematics: College Algebra. This section of material only is downloadable for a nominal fee at www.lulu.com/content/432141. See "Tell me more about Keely's GM book".
Properties of Functions
GOLDen Mathematics - College Algebra: Section 2.1
Supplemental Sites:
MathOL Links - Calg
2.1
Topics of Importance
Domain and Range
Symmetry; symmetry tests
Odd vs. even functions algebraically and graphically
Increasing, decreasing, constant functions
Local ("relative") extrema points
Comments and Cautions
This chapter forms the foundation for college algebra which is a functions
and graphs course. You should be very familiar with what a
function is and how to determine if your have a function given data in the form
of a set of ordered pairs, mapping, graph, or equation. Our goal in this class
is to expand on that basic information and concentrate on properties of
functions, learn several important new terms, study various features of
functions and their graphs, analyze the information obtained from a graph, and
use this information in practical applications.
Text Notes (These notes refer to College Algebra 4th ed by Blitzer section 2.1-2.2.)
 | ch 2.1 should be all review material from an elementary algebra course, but it is well worth reviewing this introduction to functions before we build on this information. There is quite a bit of important terminology and processes here. |
| ch 2.2 Know how to determine symmetry of a graph algebraically (via "symmetry tests") and then use this information to help you graph an equation. |
| ch 2.2 You should be able to find "Local extrema points" (also called "relative extrema points") graphically. See Calculator Guide: Extrema Points for details. Finding these points algebraically is accomplished in calculus I. |
Library of Functions
GOLDen Mathematics - College Algebra: Section 2.2
Supplemental Sites:
MathOL Links - Calg 2.2
Topics of Importance
Common functions and their graphs
Features including domain, range, increasing, decreasing, odd, even, etc.
Step functions and the greatest integer function
Piecewise functions
Power functions
Comments and Cautions
This lesson is devoted to describing various functions
and their graphs. It discusses some common functions, their graphs, and some
features of the graphs. Also introduced are some special functions that you may
not have seen before like the "greatest integer function" f(x)=
x
and "piecewise functions". The lesson includes a chart summarizing important
facts about these common and special functions and their graphs.
Text Notes (These notes refer to College Algebra 4th ed by Blitzer sections 2.3-2.5.)
| ch 2.3-2.4 should all be review from an elementary algebra course except perhaps "average rate of change" covered on page 235. This concept is a precursor to calculus where we will study "instantaneous rate of change". |
| ch 2.5 pg 242 Memorize the table! You should also be able to state, for each of the functions given: domain, range, intervals where constant, intervals where increasing, intervals where decreasing, and whether it is an odd or even function. |
Transformation of Functions
GOLDen Mathematics - College Algebra: Section 2.3
Supplemental Sites:
MathOL Links - Calg 2.3
Topics of Importance
Reflections about the x-axis, y-axis, origin
Stretch and compress
Vertical and horizontal translations
Comments and Cautions
Taking the common and special graphs learned in the last lesson,
we now transform them via reflections, stretches,
compressions, and translations (both vertical and horizontal). Pay particular
attention to how changes in the equation (changes in: coefficients, powers, and
arithmetic operations) affect its graph. Look for patterns and make connections.
Take advantage of the technology available to quickly graph the transformed
equations and make comparisons :)
Text Notes (These notes refer to College Algebra 4th ed by Blitzer section 2.5.)
| ch 2.5 pg 250 Rather than memorizing the given table you should recognize the transformations in your own terms. For instance f(x)=x2+3 is a parabola shifted up 3 since the 3 is added to the outside of the function whereas f(x)=(x+3)2 is a parabola shifted left 3 since the 3 is added to the inside of the function. Can you describe the remainder of the table in terms such as these? |
Composite and Inverse Functions
Textbook correspondence: Chapter 2.6-2.7
GOLDen Mathematics - College Algebra: Section 2.4
Supplemental Sites:
MathOL Links - Calg 2.4
Topics of Importance
Evaluate composition of functions (given equations, list of
ordered pairs, or graphs)
Determine if a relation is one-to-one (given a list of ordered pairs, graph,
or equation)
Inverse functions: determine if f-1 exists, find f-1
algebraically, verify f-1 algebraically
Comments and Cautions
This material should all be review from elementary/intermediate algebra, but
this is your opportunity to get it down pat! It forms the basis for our work
with various special functions in the remainder of this course. Use this
checklist
web.clark.edu/skeely/FILES/PDF/111/checklist_fnsgrfs.pdf to be sure that you
know all that you should about functions and graphs.
Text Notes (These notes refer to College Algebra 4th ed by Blitzer section 2.6-2.7.)
| ch 2.6-2.7 should be all review material from an intermediate algebra course, but it is extrememly important to know this material well, so definitely worth reviewing and working lots of practice problems. |
Originally written: 2006-09-04
Last revision:
2008-06-02 01:02 AM