Calculus, 8th Edition,stewart; page 43 problem 19

Question

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in section 1.2, and then applying the appropriate transformations.

y = sin (1/2x)

Answer 1

Step:1

The function is .

The function is a sine function.

The standard form of the sine function is .

Graph :

Graph of the sine function  :

Step:2

The function is .

Now substitute  instead of  in the sine function.

So .

Horizontal shrink : , stretch the graph of  horizontally by a factor of .

Therefore,  is the graph of  horizontally stretch by a factor of .

Graph :

Graph of the function .

(1) Draw the coordinate plane.

(2) Graph of the function .

(3) Stretch the graph of  horizontally by a factor of .

Solution:

Graph of the function  is

.