The photograph above shows an oriental dragon. Your job is to find a function y = f(x) describing the outer curve formed by the neck of the dragon until the neck curves back on itself and find the length of that segment. 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.
You must enter three items in the form below to describe the curve formed by the dragon. The first two items specify the domain of the function f(x) and, thus, the part of the photograph above containing the curve formed by the dragon's neck. 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 dragon's neck, discuss why it does not do as good a job as you might have hoped.
If you'd like to see a sample solution clink on this link sample solution.