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

##### 1 Answer

Start with a graph of

graph{y=arctan(x) [-10, 10, -5, 5]}

Then stretch it horizontally by a factor of

graph{y=arctan(x/3) [-10, 10, -5, 5]}

#### Explanation:

Consider a graph of a function

Let's see how this graph is related to a graph of a function

Assume, point

Then

We see now that for every point

Think now about a transformation of stretching a graph horizontally by a factor of

Therefore, you can graph a function

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.