SOLUTION: Create a function y=f(x) that has a removable discontinuity at x=2 and a non-removable discontinuity x=3.

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Question 1147401: Create a function y=f(x) that has a removable discontinuity at x=2 and a non-removable discontinuity x=3.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The removable discontinuity at x=2 means there are factors of (x-2) in both numerator and denominator.

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

Other than that the rational function can have any other factors you want. But basically the function is

f%28x%29+=+%28x-2%29%2F%28%28x-2%29%28x-3%29%29

graph%28400%2C400%2C-5%2C5%2C-2%2C2%2C%28x-2%29%2F%28%28x-2%29%28x-3%29%29%29

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.