Math 191 - Chapter 2

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Section 2.1 – A Two-Dimensional Coordinate System and Graphs
- Read pp. 134 – 143
- online resources:
  1. The Distance and Midpoint Formulas - http://www.valleyview.k12.oh.us/vvhs/dept/math/distmid.html
    This site provides a proof of the distance formula and the visual representations of both formulas.
  2. Drawing Plane and Coordinate System - http://www.univie.ac.at/future.media/moe/galerie/zeich/zeich.html
    This site provides a java applet for dynamically showing the relationship of the coordinates of a point and the position of a point on a coordinate system.
  3. Circles - http://members.shaw.ca/ron.blond/TLE/QR.DRAWCIRCLE.APPLET/
    This site provides a java applet for graphing a circle from its standard form.
  4. GraphIt - http://occawlonline.pearsoned.com/bookbind/pubbooks/billstein_awl/medialib/shodor_site/activities/graphit/index.html
    This site provides a java applet for grapher for ploting points or graphing functions. This can be used to estimate x- and y-intercepts. (To type in function y = 3x² - 2x + 5, you will need to enter 3*x*x - 2*x + 5.)
  5. Simple Plot - http://occawlonline.pearsoned.com/bookbind/pubbooks/billstein_awl/medialib/shodor_site/activities/simpleplot/index.html
    Need java-enabled browser. This site provides a grapher to plot points on a rectangular coordinate system.
Section 2.2 – Introduction to Functions
- Read pp. 147 – 158
- online resources:
  1. Function Evaluator - http://www.math.ksu.edu/math791/fv/FctApp.html
    This site provides a function evaluator so that you can enter any function of x into this applet and evaluate it at 4 points.
  2. gcalc - http://www.nsci.plu.edu/~jkim/GCalc/
    This site provides java-based grapher. This can be used to find domain of a function.

Section 2.3 – Linear Functions
- Read pp. 164 – 174
- online resources:
  1. Slope-Intercept Solver - http://webdeveloper.earthweb.com/repository/javascripts/2002/01/72571/xyxyplot.html
    This site provides the details of finding the equation for a graph in the form y=mx+b when you are given two points on the graph.
  2. Slope, Equation & y-Intercept - http://www.gomath.com/exercises/SlopeEquationYintercept.asp
    This applet shows how to find the equation of a line using user-inputed two points or a point and the slope.
  3. Function Plotter - http://www.univie.ac.at/future.media/moe/fplotter/fplotter.html
    After entering one or more functional expressions, the graphs are drawn. Using the zoom option, you may study the graphs from a very "close" viewpoint and read off coordinates of interesting points with an accuracy of about 10^-14.

Section 2.4 – Quadratic Functions
- Read pp. 180 – 187
- online resources:
  1. Names of Polynomials - http://mathforum.org/dr.math/problems/rohan.05.22.99.html
    This site provides a very good explanation of why second degree polynomials are called quadratic functions.
  2. Quadratic Function - http://members.shaw.ca/ron.blond/QFA.CSF.APPLET/
    This site provides a java grapher that shows the results of changing a, h and k in the standard form of quadratic functions.
  3. Understanding Quadratic Functions - http://www.math.uri.edu/~pakula/quadslide.htm
    This site provides java grapher that shows the results of changing a, h and k in the standard form of quadratic functions or the results of changing a, b, and c in ax² + bx + c = 0.
  4. Various Forms of a Quadratic Function: Completing the Square - http://science.kennesaw.edu/~plaval/Fall2001/m1113/wquad/node2.html
    This site provides java grapher that it similar to the above site, but it also includes a description on how to complete the square.
  5. Completing the Square I - http://school.discovery.com/homeworkhelp/webmath/polycs.html
    This site provides a solver to complete the square of polynomials. The solver shows all steps in completing the square.
  6. Completing the Square II - http://www.csm.astate.edu/algebra/csq.html
    This site provides practice problems for completing the square of polynomials. The applet shows all steps in completing the square.

Section 2.5 – Properties of Graphs
- Read pp. 192 – 201
- online resources:
  1. Shifting & Scaling (with GraphExplorer) - http://www.langara.bc.ca/mathstats/resource/GraphExplorer/v111/ShiftAndScale.html
    This site provides a java grapher so that you can enter any function and translate, reflect, shrink or stretch the graph of the function. (To type in function y = 3x² - 2x + 5, you will need to enter 3*x^2 - 2*x + 5.)
  2. New Functions from Old: Scaled and Shifted Functions - http://people.hofstra.edu/faculty/Stefan_Waner/calctopic1/scaledgraph.html
    This site provides a description for the translation, reflection, shrinking or stretching of the graph of a function.

Section 2.6 – The Algebra of Functions
- Read pp. 205 – 212
- online resources:
  1. Function Plotter - http://www.univie.ac.at/future.media/moe/fplotter/fplotter.html
    After entering one or more functional expressions, the graphs are drawn. Using the zoom option, you may study the graphs from a very "close" viewpoint and read off coordinates of interesting points with an accuracy of about 10^-14.
  2. MultiGraph Applet - http://www.calvin.edu/~rpruim/courses/m161/F01/java/FunctionComposition.shtml
    This java applet explores composition of functions graphically.
  3. The Composition of f(x) & g(x): f(g(x)) or g(f(x)) - http://mss.math.vanderbilt.edu/~pscrooke/MSS/compositefunctions.html
    This site provides java-based grapher which can be used to find the algebraic and graphical result of the composition of two functions.
  4. Arithmetic Operations with Functions - http://mss.math.vanderbilt.edu/~pscrooke/MSS/combinefunctions.html
    This site provides java-based grapher which can be used to find the algebraic and graphical result of performing an operation on two functions.
  5. Derivative Definition Java Applet - http://www.csulb.edu/~wziemer/TangentLine/TangentLine.html
    This java applet shows the convergence of the difference quotient to the derivative.

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