A Family of Functions Grapher Applet

Families of Functions Applet

This applet is designed to let the student work with families of functions. It graphs a function whose definition can contain three parameters, a, b, and c. The parameters are controlled by sliders and have values between -5 and 5.

When looking at a family of functions some questions to address include:

Is there a general shape for functions in this family?
Are there special values of parameters that look very different? (We often have a special case when a parameter is zero. Sometimes integers or positive numbers behave quite differently.)
Can you describe the change that comes from shifting a specific parameter?

Some suggested families to look at:

The general quadratic function - a*x^2 + b*x + c - This is the default function.
A combination f the sin and cos curve - a*sin(x) +b*cos(x)
The sin curve with shifts - a*sin(b*x+c)
The exponential function with shifts - a*exp(b*x) +c
A function with discreet values - floor(abs(a*x+b)) + c

A sample worksheet for this applet is available. (It looks at transformations of functions.)
A second worksheet uses the applet to look at a library of functions and to explore where in a family of functions a featyre appears.

This applet was designed as part of David Eck's "Java Components For Mathematics" project. Minor modifications were made locally.

Last modified October 18, 2004, by Mike May, S.J.