# How do you graph and find the domain and range of f(x)=log_2(x+1)+3?

Oct 16, 2016

Domain is )-1, +oo(
Range is )-oo, +oo(

#### Explanation:

f(x)=log₂(x+1)+3
A log is always $> 0$
So $x + 1 > 0$ $\implies$ $x > - 1$
So there is a vertical asymptote at $x = - 1$
And the domain is )-1, +oo(
And there is no restriction on the range )-oo, +oo(
You can see this on the graph

graph{log(x+1) +3 [-10, 10, -5, 5]}