On the grid below, graph the function... Do you always expect me here?

x intercept   =   where y = 0  .....so

0  = log₂(x - 3) + 1

-1  =  log₂(x - 3)

In exponential form

2^(-1)  = x - 3

(1/2)  = x - 3

(1/2) + 3  = x intercept  =  3.5

y intercept.....none

Increases from right to left on the domain

Domain  (3, infinity)

Range.....all reals

Asymptotes   x  = 3

End behavior    :  down on the left....up on the right