ELEMENTARY & INTERMEDIATE 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: Elementary Algebra. This section of material only is downloadable for nominal fee at www.lulu.com/content/431026. See "Tell me more about Keely's GM book".
Introduction to Graphing
GOLDen Mathematics - Elementary Algebra: Section 3.1
Supplemental Sites: MathOL Links - Alg 3.1
Topics of Importance
Graphing terminology: axes, quadrants, points, coordinates,
intercept pts, origin, signs of coordinates in quadrants
Analyzing graphs that represent real-life data
Points 
lines
Graphing by the plug-n-chug method
Introduction to modeling real-life data that grows linearly
Comments and Cautions
Mathematics can be represented
algebraically (with variables and equations as we have been doing), numerically
(with tables of data), or graphically. It is this latter method on which we
concentrate today. Concentrate on the graphing related terminology. Then move to
plotting points, then graphing lines by making a plug-n-chug chart. But by the
end of this course you will be expert graphers analyzing mathematical
applications by hand as well as by using a graphing calculator or related
electronic graphing devise. The next few sections of material are visually
inspiring which is a pretty cool way to learn algebra!
Text Notes (These notes refer to Introductory & Intermediate Algebra for CS 3rd ed by Blitzer sections 3.1.)
 | ch 3.1 begins with important terminology of graphs and graphing. It then covers plotting points and checking if a point is a solution to an equation, i.e. if the point lies on the graph of the equation. |
| ch 3.1 Starting at the bottom of page 201 the text covers graphing an equation by the "plug-n-chug chart" method. The charts of data points introduced in example 5 are often called "plug-n-chug charts" since you are plugging in x-values and chugging out y-values (or visa versa). This text calls the "plug-n-chug" method of graphing "point-plotting"; either way it means to generate a table of points, plot them, and connect to form the line. This method is useful for graphing any equation not just lines! |
| ch 3.1 example 8 is an interesting read but IMO too advanced for this level class. You will not be tested on "mathematical modeling". |
*** You will need a graphing calculator or access to an electronic grapher
for the remainder of this course. ***
My online
Calculator Guide:
Introduction to Graphing (password protected -
see password info.) contains information for students new to the
graphing calculator, just wanting a graphing calculator quick refresher, or
intending to use a (free) online graphing program instead. You may want to skim
this webpage now and cover it more thoroughly on the day it is linked from the
course calendar.
Solving Equations Graphically
GOLDen Mathematics - Elementary Algebra: Section 3.2
Supplemental Sites: MathOL Links - Alg 3.2
Topics of Importance
Graph equations electronically (including GRAPH, WINDOW, TRACE,
intercept pts, EVAL, ZOOM)
Solve equations graphically (INTERSECTION/ISECT, ZERO/ROOT)
Special cases graphically: "no solution" vs "all solutions"
Comments and Cautions
This section is graphing
calculator intensive. There are two ways to solve equations graphically, the
intersection method and the zero method. Solving equations graphically by the
intersection method involves graphing each side of the equation as a separate
curve and then using INTERSECTION or ISECT on a calculator to find the
intersection point. Solving equations graphically by the zero method involves
moving all the terms to one side of the equation, graphing it, then using ZERO
or ROOT on a calculator to find where the curve intersects the x-axis. See my
online Calculator
Guide: x-Intercept Points and
Calculator Guide:
Intersection Points for detailed calculator steps that will help you to solve an equation graphically by these two methods.
Enjoy!
Text Notes (These notes refer to Introductory & Intermediate Algebra for CS 3rd ed by Blitzer sections N/A.)
| THIS TOPIC IS NOT COVERED IN THE BLITZER TEXT AND THUS IS OMITTED FROM THIS CLASS. |
| A "contradiction" occurs when an equation has NO solution (eg. the graphs produced by the two sides of the equation are parallel lines and never intersect). An "identity" occurs when the equation has an INFINITE NUMBER of solutions (e.g. the graphs produced by the two sides of an equation are the same curves, one atop the other). These are often called the "special cases". |
Functions - Introduction
GOLDen Mathematics - Elementary Algebra: Section 3.3
Supplemental Sites: MathOL Links - Alg 3.3
Topics of Importance
Definition of relation, function, domain, and range
Determine if a relation is a function or not given: set of ordered pairs,
mapping, graph, or equation
Find domain and range given: set of ordered pairs, mapping, graph, or equation
Function notation
Evaluating functions
Function operations
Comments and Cautions
Today we will introduce the
concepts of functions and relations. There are lots of little pieces of
information here, but try to see the big picture. We will be offered relations
in the form of sets of ordered pairs, mappings, graphs, or equations, but try to
see them as just different ways to visualize the same information. As you think
about this material over the next few days, look around you for functions in the
real-world. They are everywhere!
This is a vital section since the remainder of this course and intermediate algebra deal with different types of functions and their graphs. There is lots of important terminology here. Be sure you well versed in recognizing functions given a set of ordered pairs (e.g. why is {(0,1),(0,2),(1,3),(2,3)} not a function?), a mapping, a graph (using the VLT), or an equation (which you can just graph and determine visually).
NOTATION CAUTION: f(x) ... that is "f of x" ... does not mean f times x! It does mean the equation is a function called f and the input variable is x. You can think of "f(x)" as meaning "y".
Text Notes (These notes refer to Introductory & Intermediate Algebra for CS 3rd ed by Blitzer sections 8.1-8.3.)
| ch 8.1-8.2 Spend lots of time on these very important sections which contain new terminology, notation, and processes! |
| ch 8.1-8.3 Caution: The text covers foil before functions, but the Clark elementary algebra curriculum covers functions first. So we jumped ahead to chapter 8 to pick up functions but the text includes foil in some of the exercises. THERE WILL BE NO FOIL PROBLEMS ON THIS WEEK'S QUIZ! We'll leave those until after we cover foil later in the course. So there will be NO problems such as simplify a function that has a binomial times a binomial like (x+2)(x-1) because to do that multiplication involves foil. You can SKIP any exercises that involve multiplying a binomial times a binomial. |
| ch 8.2 focuses on finding domains and ranges of functions/graphs and writing those sets in interval notation. |
| ch 8.3 pg 576 summarizes the four basic ways of algebraically combining functions. Pay attention to the notation. Example 4 provides a good overview of the processes. |
| ch 8.3 Knowing how to find the domain of a single given function (e.g., example 1 pg 575) is important. But finding the domain of a combined function (e.g., example 3b pg 377) is optional. |
| ch 8.3 skip example 5 and similar application problems in this section. These are covered in a 100-level math course. |
Originally written: 2006-006-15
Last revision:
2009-01-03 06:51 PM