What are the domain and range of the function f (x) = 3x + 5?

There is no restriction on the domain (x values) as this is a line and is continuous for all real values of x thus the domain is:

x = (-oo, + oo) or if you prefer: - oo≤x≤+oo

Since there is no restriction on the domain there is also in this case no restriction the range.

As x approaches - oo, y approaches - oo and as x approaches + oo, y approaches + oo so the range is:

y = (-oo, + oo) or - oo≤y≤+oo

Lastly you could just say that the range and domain both contain all real numbers.

I think you meant f (x) = 3^x+5, right? Write it out more clearly next time so you can get correct answers.