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Chapter 2 - Graphing Linear Relations and Functions
Concept or Definition of a Function
- Coolmath.com Function Lesson A nice, easy to follow
introduction to functions. Has 3 pages, you
will go to page 2 by clicking on "Next" at the bottom of page 1, etc.
- Edward Zobel's Definition of a Function This explanation
is a little more advanced. It goes into more detail about the domain being the set of
inputs to a function, and the range being the set of outputs. Just scroll down, the
lesson is on one long page.
- Eldred Marshall's Function Machines A nice
set of live "mathematical" function machines. Play with them and you will see why
an input/output machine works well for understanding the concept of a function. Requires
A very neat "live" graphing tool (click here). It is very similar to your graphing
calculator, but of course the screen is much bigger -- and you can print it! Make sure to
enter your expressions with an asterisk (*) for multiplication. By the
Shodor Education Foundation, Inc.
This interactive slope calculator requires the Shockwave Plug-in for your browser, the
download and installation should be almost automatic if you do not have it already.
The slider bars allow you to change the slope parameters.
Make sure to click on the "options" check boxes, there is one for "show
delta x and delta y", one for "compute slope", and one for "show line through points."
Click here for the slope calculator. By ExploreLearning.com.
Linear Regression (Least Squares) Exercise
This exercise is intended to replace the Graphing Calculator Exercise
2-5B on Page 101 and 102 of your text. The original exercise did not work
as written with the TI-83 Plus and it did not let you see what what behind
the calculation of the linear regression line. This exercise uses the
data from Problem 2 on Page 102 and shows you how to do the linear
regression on the TI-83 Plus and how to easily duplicate the calculations by hand
for this (or any) data set. Click here to see the activity.
Note: this exercise was done in Mathcad
and the web pages output by Mathcad look OK in Microsoft's Internet Explorer
but are not very good if you are using Netscape's browser. I think you can get through
it using Netscape. Older browsers won't work either. Hopefully Mathsoft
will release a more compatible conversion program at which time I'll repost this exercise.
If you have Mathcad or Mathcad Explorer (a free viewer) you are welcome to download the native
Mathcad file (click here).
Linear Regression (Least Squares) Online Activity
This demonstration of a "least squares" linear regression shows visually
what it means to fit a least squares line to a set of scatter plot points on the x-y coordinate
plane. The best "least squares" fit will result in the smallest total area of
all of the squares "on the line." The area of an individual square "on the line"
is a measure of how close the "best fit" line comes to the individual scatter plot point.
The Activity allows you to play with the best fit line and even drag the points around. The
demo was made using a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's
Sketchpad. Click here to see the activity.
Another Interactive Linear Regression (Least Squares) Online Activity
A very well done interactive "least squares" activity that lets you start
with a scatter plot, guess at a best fit line, and then see the Least Squares Fit
superimposed on the same graph. Requires Shockwave Plug-in.
Click here to see the activity.
Definition (click here).
This definition is provided at Weisstein's site which includes a very
good glossary of mathematical terms. Site is by Eric W. Weisstein and Wolfram Research, Inc.
Sponsored by Wolfram Research, Inc., makers of Mathematica
Greatest Integer Function
A Java Applet is at Manipula Math that provides a live
"Greatest Integer Function." Click here for the Greatest Integer Function.
The [x] symbol is called Gauss' Symbol. Carl Gauss is accepted by some as
one of the three greatest mathematicians that ever lived. Click here for
a biography of Gauss. The biographical link is to the web site of Trinity College at Dublin, Ireland.