Chapter 4.5, Problem 53E

To determine

To sketch: the graph of the given function..

Explanation of Solution

Given information:

Given function is

  $y=2-\sin \frac{2\pi x}{3}$

Concept used:

For the standard equation is $y=a\sin \left(bx-c\right)+d$ .

Amplitude is $\left|a\right|$ and period is $\frac{2\pi }{b}$ .

Vertical shift is $d$ unit and horizontal shift is $\frac{c}{b}$

Calculation:

Consider the function $y=2-\sin \frac{2\pi x}{3}$ .

For the given function,

  $a=1,b=\frac{2\pi }{3}$

Amplitude $=1$

Period $=\frac{2\pi }{\frac{2\pi }{3}}=3$

Now let us plot the given function,