Math 191 - Chapter 4

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Section 4.1 – Inverse Functions
- Read pp. 300 – 306
- 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)).
Section 4.2 – Exponential Functions and Their Graphs
- Read pp. 308 – 316
- 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. 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 4.3 – Logarithmic Functions and Their Graphs
- Read pp. 319 – 327
- online resources:
  1. 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.
  2. 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.

Section 4.4 – Properties of Logarithms
- Read pp. 330 – 339
- online resources:
  1. 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.
  2. 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.

Section 4.5 – Exponential and Logarithmic Equations
- Read pp. 342 – 348
- online resources:
  1. Exponential and Logarithmic Equations - http://www.okc.cc.ok.us/maustin/Exp_Log_Equations/Exponential%20and%20Logarithmic%20Equations.htm
    This site provides detailed examples for solving logarithmic or exponential equations.
  2. Some Techniques for Solving Exponential and Logarithmic Equations - http://homepage.mac.com/shelleywalsh/Math%20Articles/explog.html
    This site provides detailed examples for solving logarithmic or exponential equations.

Section 4.6 – Applications of Exponential and Logarithmic Functions
- Read pp. 353 – 361
- online resources:
  1. 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.
  2. 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.
  3. Exponential Growth - http://www.jump.net/~otherwise/population/exponent.html
    This site provides java-based applet to experiments with exponential growth.
  4. Radioactive Decay - http://home.a-city.de/walter.fendt/physengl/lawdecay.htm
    This site provides java-based simulation of exponential decay.

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