In this lesson, we will examine the domain, range, and vertical asymptotes of logarithmic functions of the following form

f(x) = a · log_B(x + c) + d

where a, B, c, and d are constants. For the purpose of this lesson, we will assume B > 1.

We will study the basic logarithmic graph:

And its reflection, if the lead coefficient (the a term) is negative:

Then, we will discuss vertical shifting and horizontal shifting of these two graphs.