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.