Question

How do you graph `y = Arctan(x/3)`?

Answer 1

Start with a graph of `y=arctan(x)`.
graph{y=arctan(x) [-10, 10, -5, 5]}
Then stretch it horizontally by a factor of `3`.
graph{y=arctan(x/3) [-10, 10, -5, 5]}

Explanation:

Consider a graph of a function `y=f(x)` as given.
Let's see how this graph is related to a graph of a function `y=f(x/k)`, where `k>1`.

Assume, point `(a,b)` belongs to a graph of function `y=f(x)`. It means that `b=f(a)`.
Then `b=f((ak)/k)`, which means that point `(ak,b)` belongs to a graph of function `y=f(x/k)`.

We see now that for every point `(a,b)` that belongs to a graph of function `y=f(x)`, graph of function `y=f(x/k)` contains a point `(ak,b)`.

Think now about a transformation of stretching a graph horizontally by a factor of `k>1`. It means that every point with coordinates `(a,b)` will be transformed into a point `(ak,b)` - exactly as happens with a graph of function `y=f(x/k)`, if compared with a graph of function `y=f(x)`.

Therefore, you can graph a function `y=f(x/k)` by starting from a graph of `y=f(x)` and stretching it horizontally by a factor of `k`.

I can recommend the Web-based course of advanced mathematics at Unizor, where a chapter linked to menu items Algebra - Graphs explains this in details.
You can also refer to chapters on Trigonometry with a relatively detailed description of all trigonometric functions and their graphs.