Question

Apply the methods of this and the previous section to graph each function. Be sure to label key points and show at

least two periods.

$y=2\tan \left(4x-\pi \right)$

Short answer

The graph of the given function is:

Step-by-step solution

Step 1. Find amplitude, period, phase shift.

Comparing the given function from general tan function i.e., $y=A\tan \left(\omega x-\varphi \right)$, we get:

$A=2$

Time period,

$$\begin{gathered} T=\frac{2\mathrm{\pi }}{\omega } \\ T=\frac{2\mathrm{\pi }}{4} \\ T=\frac{\mathrm{\pi }}{2} \end{gathered}$$

Phase shift:

$\frac{\varphi }{\omega }=\frac{\pi }{4}$

Step 2. graph the function

The graph is given by: