Question

In Problems 35-38, find the amplitude, period, and phase shift of each function. Graph each function. Show at least two periods.

$y=-\frac{2}{3}\cos (\pi x-6)$

Short answer

The amplitude, time period , phase shift is $\frac{2}{3},2,\frac{6}{\mathrm{\pi }}$respectively and the graph is

Step-by-step solution

Given information

Given function$y=-\frac{2}{3}\cos (\pi x-6)$

Comparing with y=Acos(bx-∅)+Band calculating

Comparing, we get

$$\begin{gathered} A=\frac{2}{3} \\ T=\frac{2\mathrm{\pi }}{\mathrm{\pi }} \\ T=2 \\ \frac{\varnothing }{\mathrm{\omega }}=\frac{6}{\mathrm{\pi }} \end{gathered}$$

Sketching the graph

Sketching, we get