BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.3, Problem 22E
To determine

To sketch: The function y=tanx by hand without plotting any points and then graph of the function y=14tan(x14) .

Expert Solution

Explanation of Solution

The standard graph of the function y=tanx is roughly drawn as shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.3, Problem 22E , additional homework tip  1

Then, draw the graph of y=tan(x14) , shift the graph y=tanx by π4 units to the right. Thus, the graph of y=tan(x14) is shown below in Figure 2.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.3, Problem 22E , additional homework tip  2

From Figure 2, it is observed that Figure 1 is shifted π4 units to the right. Then, draw the graph of y=14tan(x14) , shrunk the graph y=tan(x14) vertically by a factor of 4. Thus, the graph of y=14tan(x14) is shown below in Figure 3.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.3, Problem 22E , additional homework tip  3

Observe that Figure 3 is obtained from Figure 1 in such a way that it is shifted π4 units to the right and then compressed vertically by a factor of 4.

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