The photograph above is a classic
coca cola bottle. Your job is to find a function y = f(x) describing the
curve formed by the bottle. As part of describing the function f(x) you will
need to specify its domain -- that is, the lowest and highest values of the
variable x.
You can click on the photograph
above to find the coordinates of the point at which you clicked. You can fine
tune the selected point by clicking at the arrows at the four sides of the
photograph. Each click on an arrow moves the cursors one pixel in the direction
indicated by the arrow.
It is easiest to find points, and
then an equation for the top half of the bottle, and then find a separate
equation (just reflected over the x axis) for the opposite side of the bottle.
You must enter three items in the
form below to describe the curve formed by the bottle. The first two items
specify the domain of the function f(x). The third item is an algebraic expression -- like x^3 - x
+ 12, for example -- that defines the function f(x) that describes
the shape of the curve.
After you have entered the three
items in the form below, click the "Try it!!" button to see
the curve superimposed on the photograph.
After you have found a function
that you are reasonably happy with that describes the curve formed by the coca cola
bottle, discuss why it does not do as good a job as you might have hoped.