Introduction to Functions

Tutorial which is an introduction to functions including the four representations of a function, domain, and range.
• Drill on finding domains of functions.
• Computer program to visualize a function as "a collection of arrows from the domain to the range."

Piecewise Defined Functions

Tutorial on piecewise defined functions.

Even and Odd Functions

Tutorial on even and odd functions.
• A LiveMath Notebook to visualize when a function is symmetric with respect to the y-axis.
• A LiveMath Notebook to visualize when a function is symmetric with respect to the origin.
• A LiveMath Notebook to determine which function in a family of functions is odd.
• A quiz on determining which functions are even, odd or neither.
• Computer programs to determine graphically whether a function is even or odd or neither.

Polynomials

Tutorial on polynomial functions.

Rational Functions

Tutorial on rational functions.

Geometric Transformations of Functions

Tutorial on the translation, compression, stretching and reflection of graphs of functions.
• A Java applet to explore graphically the effect of transforming a graph with translations, vertical and horizontal stretching and reflections.
• A quiz to explore graphically the effect of transforming a graph with translations, vertical and horizontal stretching and reflections.
• Given a function, draw the graphs of functions obtained by shifting the graph of a given function using the
• Computer programs that will easily draw the graphs of functions obtained by shifting the graph of a given function.
• Computer programs that will easily draw the graphs of functions obtained by shifting the graph of a given function.

Algebra of Functions

Composition of Functions

Tutorial on the composition of functions.

Trigonometric Functions

• A listing of trigonometric identities.
• Computer programs that draw the graphs of trigonometric functions, sine and cosine, considered as circular functions.
• Computer programs that draw the graph of the tangent function considered as circular functions.

Exponential Functions

Tutorial on exponential functions.

Inverses of Functions

Tutorial on inverses of functions.
• A Flash movie illustrating the use of the horizontal line test and the finding the equation of the inverse of a function.
• Using Maple to find explicitly the inverse of a function and verify that it is the inverse.
• A LiveMath Notebook to investigate which polynomials of degree 3 have inverses.
• Drill on finding the inverses of functions.
• Drill in finding the inverses of functions (includes inverse trigonometric functions).
• Computer programs that will draw the graph of a function and its inverse. Also,

Logarithms

Tutorial on logarithms.
• A LiveMath animation of a family of logarithmic functions.
• LiveMath animations to explore graphically and symbolically the effect of transforming logarithmic functions.
• A Java applet to explore graphically and symbolically the effect of transforming logarithmic functions.
• Computer programs that draw the graphs of the exponential and logarithm functions in order to visualize that they are inverses of each other.

Parameters and Functions

Tutorial on familes of functions with parameters.

Parametric Equations

Tutorial on parametric equations.

Polar Coordinates

Tutorial on polar coordinates.

Graphing with Technology

Tutorial on how computer programs and graphing calculators plot the graphs of functions and some of the problems that this method of plotting has.
• Problems in using a computer to draw the graph of a function. In this example, changing the number of points used in drawing the graph changes the graph significantly.
• Slide show on which the page above is based.
• A LiveMath notebook showing some problems in using a computer to draw the graph of a function. In this example, zooming in shows some features of the graph otherwise missed.
• Computer programs and their problems in drawng the graph of a function with a discontinuity.
• Computer programs and their problems in drawng the graph of the rational power of a variable.
• Computer program that will plot the graph of a finite collection of ordered pairs.

Solving Equations

Tutorial on finding the intersections of the graphs of two functions.

Curve Fitting

Tutorial on curve fitting.

Conic Sections

• Computer programs that draw the graphs of various conic sections.
• Computer programs that draw the graphs of various conic sections using polar coordinates.
• A review of the concept of eccentricity through examining the effects of changing the value of the variable e in the polar equation of an ellipse.