Describe the Squirt

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The photograph above shows water squirting from a water fountain. Your job is to find a function y = f(x) describing the curve formed by the squirting water. 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 on the arrows at the four sides of the photograph -- each click moves the cross hairs 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 squirting water. 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 squirting water. The third item is an algebraic expression -- like 3*x^3 - 2*x + 12, for example -- defining the function f(x) that describes the shape of the curve. (Note that only the defining expression is entered, not "f(x) =" or anything else.)

After you have entered the three items in the form below, click the "Try it!!" button to see the curve superimposed on the photograph.

Low end of the domain
High end of the domain
The function f(x)

After you have found a function you are reasonably happy with that describes the curve formed by the squirting water, discuss why it does not do as good a job as you might have hoped.