# How do you find the amplitude, period, and shift for y=4tan(2x-pi)?

Mar 17, 2016

The amplitude is 4, the period is $\frac{\pi}{2}$, and the graph is shifted to the right $\frac{\pi}{2}$.

#### Explanation:

The general pattern for a tangent function is:
$y = a \tan b \left(x - h\right) + k$

In this case, $a$ is 4, so the amplitude is 4.

To find the period, we need to find the $b$ value first. To do this, we need to pull out the 2 in order to isolate $x$. Therefore, we get:
$y = 4 \tan 2 \left(x - \frac{\pi}{2}\right)$
The period for a tangent function is equal to $\frac{\pi}{b}$.
$\frac{\pi}{b} = \frac{\pi}{2}$

The $h$ value is how much the graph is shifted horizontally. In this case, we can see that the graph is shifted to the right $\frac{\pi}{2}$.