Explanation Given: The graph of the function f ( x ) = sin x is compressed horizontally by a factor of 2 and then shifted 5 units to the right. Calculation: Part a: The function is: f ( x ) = sin x The function f ( x ) = sin x is compressed horizontally by a factor of 2 and then shifted 5 units to the right. We know that y = f ( k x ) , if k > 1 then the graph is compressed in the horizontal direction. So, k = 2 > 1 . Thus, y = f ( 2 x ) Also, we know that, y = f ( x − c ) , this shifts the graph of f ( x ) horizontally c units to the right. So, the function shifted 5 units to the right. Thus, y = f ( 2 ( x − 5 ) ) The function becomes, y = f ( 2 x − 10 ) = sin ( 2 x − 10 ) We can rewrite it as: g ( x ) = sin ( 2 x − 10 ) Hence, the function g ( x ) = sin ( 2 x − 10 ) . Part b: The function is: f ( x ) = sin x Now, we have to find the new equation. The graph shifted 5 units to the right. y = f ( x − 5 ) Now, compressed by 2. y = f ( 2 x − 5 ) So, the function becomes y = sin ( 2 x − 5 ) We can rewrite it as: g ( x ) = sin ( 2 x − 5 ) Hence, the function g ( x ) = sin ( 2 x − 5 ) . Part c: First, find the points to draw the graph of the function g ( x ) = sin ( 2 x − 10 ) . We can rewrite it as: y = sin ( 2 x − 10 ) Put x = 0 in the given function

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 1.1, Problem 73E

To determine

a. What is the equation of the new graph?

b. What is the equation if you first shift by 5 and then compress by 2?

c. Check your answers by draw the graph of equations.

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Chapter 1.1, Problem 72E

Chapter 1.1, Problem 74E

Chapter 1 Solutions

Calculus - Standalone book

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - 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a. What is the equation of the new graph? b. What is the equation if you first shift by 5 and then compress by 2? c. Check your answers by draw the graph of equations.

Solution Summary: The author explains how the graph of the function g(x)=mathrmsin left is compressed horizontally by a factor of 2 and then shifted 5 units to the

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a. What is the equation of the new graph? b. What is the equation if you first shift by 5 and then compress by 2? c. Check your answers by draw the graph of equations.

Want to see the full answer?

Chapter 1 Solutions

a. What is the equation of the new graph?

b. What is the equation if you first shift by 5 and then compress by 2?

c. Check your answers by draw the graph of equations.