# How do you graph #y=log_2(x-1)+3#?

##### 1 Answer

**Step 1: Determine the coordinates of any asymptotes, the domain and the range**

Let's start with what's easiest. The range of every logarithmic function is

The domain is a little trickier. It is now that asymptotes come into play. A vertical asymptote will occur when

Hence, there will be a vertical asymptote at

**Step 2: Determine any reflections, compressions, stretches and horizontal and/or vertical tranformations**

This is a part that is important, but that many people choose to neglect. They will instead use a table of values, which can be helpful. But let's first look at the transformations that appear when converting the function

First, you'll notice that the graph has undergone a horizontal transformation of

Now that we know this, we can plot a table of values and understand the trend relative to

After doing this, you'll end up with the following graph:

Hopefully this helps!