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

Sep 22, 2015

I found:
Domain: all real $x$ except $x = 3$;
Range: $- \infty <$$x$$< 0$ or $0 <$$x$$< + \infty$

#### 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 $- \infty$ to $- \infty$ getting as near as possible to zero without ever reaching it!

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