functions of the form
f(x) = a / [ 1 + b e - (x - c) / d ]
are explored along with the properties of their graphs.
Parameters a, b, c and d, defining function f are changed and their effects analyzed.
1 - click on the button above "draw" to disply the graph of the logistics function.
2 - What happens to the graph of the function as x increases? Change parameter a and see what happens. Find an analytical explanation.
3 - Set parameters a, b and d to constant values and change c. What happens to the graph? Find an analytical explanation.
4 - Set parameters to constant values and change d. What happens to the graphs? Find an analytical explanation.
ANSWERS TO THE ABOVE QUESTIONS
2 - As x starts from negative values and increases, f(x) starts from values close to zero then approaches a constant value equal to parameter a. y = a is a horizontal asymptote.
3 - The whole graph is shifted to the right when c increases and to the left when c decreases.
4 - For small values of d, the graph changes rapidly. For larger values of d the graph changes slowly.