Question 1041912
Only one critical value for x, at x=3, where f is undefined.


The domain is the union, as you found.


RANGE:
What can be f, near but less than 3?  What can be f, farther to the left of 3?  What happens to f as x approaches 3 from the left?
Now ask and handle the same question but on the other side of x at 3.
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Also think what happens to f as x goes unbound to the left; and what happens as x goes unbound to the right.
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You should be able to know what is the range of f, now.




{{{graph(400,400,-8,8,-8,8,2/(x-3))}}}




All real numbers EXCLUDING 0.
Range is  (-infinity,0) AND (0, infinity).



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(Range:  I believe you have it (based on your personal message - not on what is in your posting here.)