Given the information that the graph of a function has a y-intercept at (0,1) and exactly two x-intercepts at (2,0) and (4,0), how many different functions can you find that pass through these three points?

Note: there are infinite families of functions such as high degree polynomials which pass through them, so a single example would suffice for them. Also disallowed would be piecewise function and functions with artificially restricted domains.

(In reply to re: The Old Kitchen Sink by Jer)

Sorry, I was just concentrating on the "pass through these three points" part of the question, and missed the "exactly two" part.  By the way, aren't these "x-intercepts" of yours usually called "zeros" and isn't "x-intercept" reserved for linear functions that have one and is never used in the plural?

Posted by Richard on 2006-06-20 15:34:43