Chapter C, Problem 37E

To determine

To graph:

The following function with the help of the transformation:

  $y=\cos \left(x-\frac{\pi }{3}\right)$

Explanation of Solution

Given information:

  $y=\cos \left(x-\frac{\pi }{3}\right)$

Graph:

  

Graph 1: $y=\cos x$

  

Graph 2: $y=\cos \left(x-\frac{\pi }{3}\right)$

Interpretation:

Need to draw a first graph of the function $y=\cos x$ as shown by the graph 1. Now, the given function $y=\cos \left(x-\frac{\pi }{3}\right)$ is in form of the $y=f\left(x-c\right)$ . It means that need to shift the graph by $y=f\left(x\right)c$ on the right side.

Hence, the graph shifted towards right $y=\cos \left(x-\frac{\pi }{3}\right)$ with the transformation and it shown by the graph 2.