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

Question

(a) How is the graph of y = 2 sin x related to the graph of y = sin x ? Use your answer and Figure 6 to sketch the graph of y = 2 sin x.

(b) How is the graph of y = 1 + √x related to the graph of y = √x ? use your answer and Figure 4(a) to sketch the graph of y = 1 + √x.

Answer 1

Step:1

(a)

The function is .

Compare the function with .

Vertical stretch:  is the graph of  stretch vertically by a factor of .

Graph :

Graph of the function .

(1) Draw the coordinate plane.

(2) Graph the function .

(3) Now stretch the graph of  vertically by a factor of .

Step:2

(b)

The function is .

Compare the function with .

Vertical shift :  is the graph of  shift to a distance  unit upward.

Graph :

Graph of the function .

(1) Draw the coordinate plane.

(2) Graph the function .

(3) Now shift the graph of  to a distance  unit upward.

Solution:

(a) Graph of the function .

Stretch the graph of  vertically by a factor of .

(b) Graph of the function .

Shift the graph of  to a distance  unit upward.

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