Math 195 - Chapter 1

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Section 1.1 – Four Ways to Represent a Function
- Read pp. 11 – 21
- online resources:
  1. GCalc Free Online Graphing Calculator - http://www.nsci.plu.edu/~jkim/GCalc/
    This site provides a java applet in which more than one equation can be graphed.
  2. Plotting Functions on the same Graph - http://mss.math.vanderbilt.edu/~pscrooke/MSS/plotseveral.html
    This site provides a java applet in which more than one equation can be graphed.
  3. 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.
Section 1.2 – Mathematical Models
- Read pp. 24 – 35
- online resources:
  1. GCalc Free Online Graphing Calculator - http://www.nsci.plu.edu/~jkim/GCalc/
    This site provides a java applet in which more than one equation can be graphed.
  2. Plotting Functions on the same Graph - http://mss.math.vanderbilt.edu/~pscrooke/MSS/plotseveral.html
    This site provides a java applet in which more than one equation can be graphed.
  3. 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.
Section 1.3 – New Functions from Old Functions
- Read pp. 38 – 46
- 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.
  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.
Section 1.5 – Exponential Functions
- Read pp. 56 – 63
- online resources:
  1. The Exponential Function I - http://members.shaw.ca/ron.blond/TLE/ExpFcn.APPLET/
    This site provides a java applet which graphs y = a*b^x with sliders to see what happens to the graph when a and b change.
  2. The Exponential Function II - http://mathinsite.bmth.ac.uk/applet/exponential/exp.html
    This site provides a java applet which graphs y = A + Be^kx with sliders to see what happens to the graph when A, B and k change.
  3. Commonly Used Formulas - Exponents - http://campus.northpark.edu/math/PreCalculus/formulas.html#exponents
    This site provides a list of the properties of exponents.
  4. Glossary - Natural Exponential Function - http://www.calonline.msstate.edu/text/glossary/#Exp%20func
    This site provides an applet which defines e^x using the derivative function.
  5. GCalc Free Online Graphing Calculator - http://www.nsci.plu.edu/~jkim/GCalc/
    This site provides a java applet in which more than one equation can be graphed.
  6. Plotting Functions on the same Graph - http://mss.math.vanderbilt.edu/~pscrooke/MSS/plotseveral.html
    This site provides a java applet in which more than one equation can be graphed.
  7. 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.
  8. Compound Interest - http://id.mind.net/~zona/mmts/functionInstitute/exponentialFunctions/compoundInterest.html
    This site provides a discussion of compound interest and a compound interest calculator.
  9. Continuous Interest - http://id.mind.net/~zona/mmts/functionInstitute/exponentialFunctions/continuousInterest.html
    This site provides a discussion of continuous compound interest and a continuous compound interest calculator.
  10. Exponential Growth - http://www.jump.net/~otherwise/population/exponent.html
    This site provides java-based applet to experiments with exponential growth.
  11. Radioactive Decay - http://home.a-city.de/walter.fendt/physengl/lawdecay.htm
    This site provides java-based simulation of exponential decay.
Section 1.6 – Inverse Functions and Logarithms
- Read pp. 64 – 72
- online resources:
  1. Inverse Functions - http://mss.math.vanderbilt.edu/cgi-bin/MSSAgent/~pscrooke/MSS/inversefunction.def
    This site provides a tool in which given a function y = f(x), it attempts to find its inverse: x = f ^-1(y).
  2. Functions and Their Inverses - http://www.mathsnet.net/asa2/modules/p22inverses2.html
    This site provides a which graphically plots the graph of f(x); its inverse, g(x); and the composition, g(f(x)).
  3. The Exponential and Logarithm Functions - http://www.cnice.mecd.es/Descartes/Ingles/expolog.htm
    This site provides various java-based graphers to investigate the properties of the graphs of exponential and logarithmic functions.
  4. Transformations of Logarithmic Functions - http://archives.math.utk.edu/visual.calculus/0/shifting.6/index.html
    This site provides a java grapher that shows the results of changing a, b, c and d in the log function f(x) = a ln(b (x - c)) + d.
  5. Properties of Logarithms - http://campus.northpark.edu/math/PreCalculus/Transcendental/Logarithmic/Properties/
    This site provides a detailed discussed with java-based graphs of the properties of log functions.
  6. Commonly Used Formulas - Logarithms - http://campus.northpark.edu/math/PreCalculus/formulas.html#logarithms
    This site provides a list of the properties of logarithms.
  7. log_aM + log_aN = log_aMN - http://archives.math.utk.edu/visual.calculus/0/shifting.6/index.html
    This site provides a java applet that graphically illustrates the sum rule for logs.

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