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.
For any nonzero integer k,
=(sin(k*pi*x/2))/(k*pi*x/2) for nonzero x,
=1 for x=0
is 1 at x=0 and is zero at when x is any nonzero multiple of 2/k
(including 2 and 4). Also, any of these can be multiplied by any
function of the real variable x which equals 1 at x=0, for example by
See MathWorld or Wikipedia entries for Sinc Function.
Edited on June 19, 2006, 10:58 pm
Posted by Richard
on 2006-06-19 22:35:30