Q. 19 - Precalculus Enhanced with Graphing Utilities

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.

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

Step-by-Step Solution

Answer

The graph of the given function is:

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: