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