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.