# What are the important information needed to graph y=3tan2x?

Apr 11, 2016

#### Explanation:

A typical graph of $\tan x$ has domain for all values of $x$ except at $\left(2 n + 1\right) \frac{\pi}{2}$, where $n$ is an integer (we have asymptotes too here) and range is from $\left[- \infty , \infty\right]$ and there is no limiting (unlike other trigonometric functions other than tan and cot). It appears like graph{tan(x) [-5, 5, -5, 5]}

The period of $\tan x$ is $\pi$ (i.e. it repeats after every $\pi$) and that of $\tan a x$ is $\frac{\pi}{a}$ and hence for $\tan 2 x$ period will be $\frac{\pi}{2}$

The asymptotes for will be at each $\left(2 n + 1\right) \frac{\pi}{4}$, where $n$ is an integer.

As the function is simply $\tan 2 x$, there is no phase shift involved (it is there only if function is of the type $\tan \left(n x + k\right)$, where $k$ is a constant. Phase shift causes graph pattern to shift horizontally to left or right.

The graph of $\tan 2 x$ appears like graph{tan(2x) [-5, 5, -5, 5]}