EBK PRECALCULUS W/LIMITS

3rd Edition

ISBN: 9781285607160

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 4.5, Problem 20E

To determine

To describe: the relationship between the graphs of $f$ and $g$ .

Expert Solution & Answer

Explanation of Solution

Given information:

Given functions are

$f(x)=cosxg(x)=cos(x+π)$

Concept used:

For the standard equation is $y=acosbx$ .

Amplitude is $|a|$ and period is $2πb$ .

Calculation:

Comparing $f(x)=cosx$ with the equation $y=acosbx$ ,

$a=1$ and $b=1$

Thus,

$Amplitude=|1|=1$

And

$Period=2πb=2π(1)=2π$

The interval $[0,2π]$ corresponds to one cycle on the graph.

The amplitude of $y=asin(bx−c)$ and $y=acos(bx−c)$ have following characteristics.

$Amplitude=|a|Period=2πb$

The left and right endpoints of one cycle interval can be determined by solving the equations

$bx−c=0$ and $bx−c=2π$

Comparing $g(x)=cos(x+π)$ with the equation $y=acos(bx−c)$ ,

$a=1$ and $b=1$

Thus,

$Amplitude=|1|=1$

And

$Period=2πb=2π(1)=2π$

The left end point is,

$x+π=0x=−π$

The right end point is,

$x+π=2πx=π$

So interval $[−π,π]$ corresponds to one cycle on the graph.

Now plot the graphs of $f(x)$ and $g(x)$ :

EBK PRECALCULUS W/LIMITS, Chapter 4.5, Problem 20E

By above graph it is seen that $g(x)$ is a shift of $f(x) π$ units to the left.

Chapter 4.5, Problem 19E

Chapter 4.5, Problem 21E

Chapter 4 Solutions

EBK PRECALCULUS W/LIMITS

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Prob. 49E Ch. 4.8 - Prob. 50E Ch. 4.8 - Prob. 51E Ch. 4.8 - Prob. 52E Ch. 4.8 - Prob. 53E Ch. 4.8 - Prob. 54E Ch. 4.8 - Prob. 55E Ch. 4.8 - Prob. 56E Ch. 4.8 - Prob. 57E Ch. 4.8 - Prob. 58E Ch. 4.8 - Prob. 59E Ch. 4.8 - Prob. 60E Ch. 4.8 - Prob. 61E Ch. 4.8 - Prob. 62E Ch. 4 - Prob. 1RE Ch. 4 - Prob. 2RE Ch. 4 - Prob. 3RE Ch. 4 - Prob. 4RE Ch. 4 - Prob. 5RE Ch. 4 - Prob. 6RE Ch. 4 - Prob. 7RE Ch. 4 - Prob. 8RE Ch. 4 - Prob. 9RE Ch. 4 - Prob. 10RE Ch. 4 - Prob. 11RE Ch. 4 - Prob. 12RE Ch. 4 - Prob. 13RE Ch. 4 - Prob. 14RE Ch. 4 - Prob. 15RE Ch. 4 - Prob. 16RE Ch. 4 - Prob. 17RE Ch. 4 - Prob. 18RE Ch. 4 - Prob. 19RE Ch. 4 - Prob. 20RE Ch. 4 - Prob. 21RE Ch. 4 - Prob. 22RE Ch. 4 - Prob. 23RE Ch. 4 - Prob. 24RE Ch. 4 - Prob. 25RE Ch. 4 - Prob. 26RE Ch. 4 - Prob. 27RE Ch. 4 - Prob. 28RE Ch. 4 - Prob. 29RE Ch. 4 - Prob. 30RE Ch. 4 - Prob. 31RE Ch. 4 - Prob. 32RE Ch. 4 - Prob. 33RE Ch. 4 - Prob. 34RE Ch. 4 - Prob. 35RE Ch. 4 - Prob. 36RE Ch. 4 - Prob. 37RE Ch. 4 - Prob. 38RE Ch. 4 - Prob. 39RE Ch. 4 - Prob. 40RE Ch. 4 - Prob. 41RE Ch. 4 - Prob. 42RE Ch. 4 - Prob. 43RE Ch. 4 - Prob. 44RE Ch. 4 - Prob. 45RE Ch. 4 - Prob. 46RE Ch. 4 - Prob. 47RE Ch. 4 - Prob. 48RE Ch. 4 - Prob. 49RE Ch. 4 - Prob. 50RE Ch. 4 - Prob. 51RE Ch. 4 - Prob. 52RE Ch. 4 - Prob. 53RE Ch. 4 - Prob. 54RE Ch. 4 - Prob. 55RE Ch. 4 - Prob. 56RE Ch. 4 - Prob. 57RE Ch. 4 - Prob. 58RE Ch. 4 - Prob. 59RE Ch. 4 - Prob. 60RE Ch. 4 - Prob. 61RE Ch. 4 - Prob. 62RE Ch. 4 - Prob. 63RE Ch. 4 - Prob. 64RE Ch. 4 - Prob. 65RE Ch. 4 - Prob. 66RE Ch. 4 - Prob. 67RE Ch. 4 - Prob. 68RE Ch. 4 - Prob. 69RE Ch. 4 - Prob. 70RE Ch. 4 - Prob. 71RE Ch. 4 - Prob. 72RE Ch. 4 - Prob. 73RE Ch. 4 - Prob. 74RE Ch. 4 - Prob. 75RE Ch. 4 - Prob. 76RE Ch. 4 - Prob. 77RE Ch. 4 - Prob. 78RE Ch. 4 - Prob. 79RE Ch. 4 - Prob. 80RE Ch. 4 - Prob. 81RE Ch. 4 - Prob. 82RE Ch. 4 - Prob. 83RE Ch. 4 - Prob. 84RE Ch. 4 - Prob. 85RE Ch. 4 - Prob. 86RE Ch. 4 - Prob. 87RE Ch. 4 - Prob. 88RE Ch. 4 - Prob. 89RE Ch. 4 - Prob. 90RE Ch. 4 - Prob. 91RE Ch. 4 - Prob. 92RE Ch. 4 - Prob. 93RE Ch. 4 - Prob. 94RE Ch. 4 - Prob. 95RE Ch. 4 - Prob. 96RE Ch. 4 - Prob. 97RE Ch. 4 - Prob. 98RE Ch. 4 - Prob. 99RE Ch. 4 - Prob. 100RE Ch. 4 - Prob. 101RE Ch. 4 - Prob. 102RE Ch. 4 - Prob. 1CT Ch. 4 - Prob. 2CT Ch. 4 - Prob. 3CT Ch. 4 - Prob. 4CT Ch. 4 - Prob. 5CT Ch. 4 - Prob. 6CT Ch. 4 - Prob. 7CT Ch. 4 - Prob. 8CT Ch. 4 - Prob. 9CT Ch. 4 - Prob. 10CT Ch. 4 - Prob. 11CT Ch. 4 - Prob. 12CT Ch. 4 - Prob. 13CT Ch. 4 - Prob. 14CT Ch. 4 - Prob. 15CT Ch. 4 - Prob. 16CT Ch. 4 - Prob. 17CT Ch. 4 - Prob. 18CT Ch. 4 - Prob. 19CT Ch. 4 - Prob. 20CT Ch. 4 - Prob. 1PS Ch. 4 - Prob. 2PS Ch. 4 - Prob. 3PS Ch. 4 - Prob. 4PS Ch. 4 - Prob. 5PS Ch. 4 - Prob. 6PS Ch. 4 - Prob. 7PS Ch. 4 - Prob. 8PS Ch. 4 - Prob. 9PS Ch. 4 - Prob. 10PS Ch. 4 - Prob. 11PS Ch. 4 - Prob. 12PS Ch. 4 - Prob. 13PS Ch. 4 - Prob. 14PS

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the relationship between the graphs of f and g .

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To describe: the relationship between the graphs of f<m:math><m:mi>f</m:mi></m:math> and g<m:math><m:mi>g</m:mi></m:math> .

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To describe: the relationship between the graphs of $f$ and $g$ .