Grade 11: Piece of Wire

pieceofwiregraph

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

Equation
pieceofwiregraph2

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).

Teacher manual
Student workbook