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

1 Answer
Sep 22, 2015

Answer:

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]}