Question

How do you find domain and range for `f(x)=5/(x-3)`?

Answer 1

I found:
Domain: all real `x` except `x=3`;
Range: `-oo<` `x` `<0` or `0<` `x` `<+oo`

Explanation:

The domain odf your function represents the set of allowed `x` values; in your case the only forbidden `x` value is `x=3` that would make your denominator equal to zero and induce a division by zero!

The range (the possible `y` values of your function) is a little bit tricky. Apparently your function will give you every value of `y` but if you consider `x` VERY large you'll see that your function will gets near zero but never reach it. So your function will give you every real value from `-oo` to `-oo` getting as near as possible to zero without ever reaching it!

Graphically:
graph{5/(x-3) [-10, 10, -5, 5]}