Question

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

Answer 1

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

Explanation:

`f(x)=log₂(x+1)+3`
A log is always `>0`
So `x+1>0` `=>` `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]}