Explanation The graph of y = f ( 1 3 x ) is a straight line passing through the origin ( 0 , 0 ) when f ( x ) = x Given: A function as y = x 3 Calculation: Consider the function y = x 3 Let us find the value of y by using the values of f ( x ) x y = x 3 -3 y ( − 3 ) = − 3 3 = -1 -2 y ( − 2 ) = − 2 3 -1 y ( − 1 ) = − 1 3 0 y ( 0 ) = 0 3 = 0 1 y ( 1 ) = 1 3 2 y ( 2 ) = 2 3 3 y ( 3 ) = 3 3 = 1 Let us now plot the points to sketch the graph of y = 1 x 2 Now consider y = f ( 1 3 x – b ) y = ( 1 3 x – b ) y = ( x – 3 b 3 ) Let us suppose value of b = 1 Thus, the function becomes y = ( x – 3 3 ) Let us find the value of y by using the values of f ( x ) x y = ( x – 3 3 ) -3 y ( − 3 ) = - 3 – 3 3 = 0 -2 y ( − 2 ) = - 2 – 3 3 = - 5 3 -1 y ( − 1 ) = - 1 – 3 3 = - 4 3 0 y ( 0 ) = 0 – 3 3 = − 1 1 y ( 1 ) = 1 – 3 3 = – 2 3 2 y ( 2 ) = 2 – 3 3 = – 1 3 3 y ( 3 ) = 3 – 3 3 = 0 Let us now plot the points to sketch the graph of y = ( x – 3 3 )

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 1, Problem 41CRE

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To show that the graph of y = f(13x – b) is obtained by shifting the graph of y = f(13x) to the right by 3b units. Use this observation to sketch the graph of y = |13x – 4|

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Chapter 1, Problem 40CRE

Chapter 1, Problem 42CRE

Chapter 1 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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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To show that the graph of y = f ( 1 3 x – b ) is obtained by shifting the graph of y = f ( 1 3 x ) to the right by 3 b units. Use this observation to sketch the graph of y = | 1 3 x – 4 |

Solution Summary: The author illustrates how the graph of y= f(13x) is obtained by shifting it to the right by 3b units.

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To show that the graph of y = f(13x – b) is obtained by shifting the graph of y = f(13x) to the right by 3b units. Use this observation to sketch the graph of y = |13x – 4|

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Chapter 1 Solutions