document.write( "Question 1147401: Create a function y=f(x) that has a removable discontinuity at x=2 and a non-removable discontinuity x=3. \n" ); document.write( "

Algebra.Com's Answer #768765 by greenestamps(13203) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "The removable discontinuity at x=2 means there are factors of (x-2) in both numerator and denominator.

\n" ); document.write( "The non-removable discontinuity at x=3 means there is a factor of (x-3) in the denominator and not in the numerator.

\n" ); document.write( "Other than that the rational function can have any other factors you want. But basically the function is

\n" ); document.write( " $\"f%28x%29+=+%28x-2%29%2F%28%28x-2%29%28x-3%29%29\"$

\n" ); document.write( " $\"graph%28400%2C400%2C-5%2C5%2C-2%2C2%2C%28x-2%29%2F%28%28x-2%29%28x-3%29%29%29\"$

\n" ); document.write( "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. \n" ); document.write( "

\n" );