Grade 11: Piece of Wire
Here is a sample problem. At the right is the graph
y = f(x), (0 ≤ x < 2)
with the following properties
f(0) = 0
f(1) = 4
f has a vertical asymptote at x = 2
The lower diagram depicts the family of curves
Here the parameter a is an integer between 1 and 10.
Suppose I tell you that the graph of f can be obtained by cutting a piece out of one member of the family y=a/x, flipping it and moving it, but not bending or deforming it in any way.
Given this, find the equation y = f(x).