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 16E
To determine

To sketch: The function y=1+sinπx by hand without plotting any points.

Expert Solution

Explanation of Solution

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

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.3, Problem 16E , additional homework tip  1

Draw the graph of y=sinπx by shrinking the graph of y=sinx horizontally by a factor of π.

Use online graphing calculator to sketch the graph of y=sinπx as shown below in Figure 2.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.3, Problem 16E , additional homework tip  2

From Figure 2, it is observed that Figure 1 is compressed horizontally by a factor of π.

To draw the graph of y=1+sinπx, shift the graph y=sinπx by 1 unit upward.

Use online graphing calculator to sketch the graph of y=1+sinπx as shown below in Figure 3.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.3, Problem 16E , additional homework tip  3

From Figure 3, it is observed that the graph of the function y=1+sinπx lies above the x-axis.

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