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

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 1.1, Problem 79E

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 78E

Chapter 1.1, Problem 80E

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Chapter 1 Solutions

CALCULUS (CLOTH)

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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.

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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.