Question 1147401
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The removable discontinuity at x=2 means there are factors of (x-2) in both numerator and denominator.<br>
The non-removable discontinuity at x=3 means there is a factor of (x-3) in the denominator and not in the numerator.<br>
Other than that the rational function can have any other factors you want.  But basically the function is<br>
{{{f(x) = (x-2)/((x-2)(x-3))}}}<br>
{{{graph(400,400,-5,5,-2,2,(x-2)/((x-2)(x-3)))}}}<br>
The removable discontinuity won't show up on the graph created by the graphing utility on this site; it will show up (as a hole in the graph) on a good graphing calculator like the TI-83.