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 The Old Kitchen Sink by Richard)

The sinc function appears to have infinitely many x-intercepts, not just two as specified.

Are you proposing to modify a sinc function?  If so, restricting its domain artificially is not allowed but transformations are.

Posted by Jer on 2006-06-20 14:50:08