Recall that the graph represented by the graph of h(x) translated horizontally n units to the left is:
[tex]f(x+n)\text{.}[/tex]
Therefore the graph of:
[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]
is the graph of
[tex]h(x)=\cot (x)[/tex]
translated π/6 units to the left.
Now, recall that the asymptotes of h(x)=cot(x) are:
[tex]x=n\pi\text{.}[/tex]
Then, the graph of h(x)=cot(x) is:
Therefore the graph of the given function is:
The asymptotes are of the form:
[tex]x=n\pi-\frac{\pi}{6}[/tex]
Answer:
The asymptotes are of the form:
[tex]x=n\pi-\frac{\pi}{6}[/tex]
