(a) Answer The domain of function is all the real numbers except x = 3 2 . Explanation Given information: The function is f ( x ) = x 2 − 3 x − 4 2 x 2 + x − 1 Calculation: Consider the function. . f ( x ) = 6 x 2 − 11 x + 3 6 x 2 − 7 x − 3 Simplify the function. f ( x ) = 6 x 2 − 11 x + 3 6 x 2 − 7 x − 3 f ( x ) = ( 2 x − 3 ) ( 3 x − 1 ) ( 3 x + 1 ) ( 2 x − 3 ) f ( x ) = ( 3 x − 1 ) ( 3 x + 1 ) The function is valid for all the real numbers except x = 3 2 and x = − 1 3 . Therefore, the domain of function is all the real numbers except x = 3 2 and x = − 1 3 . (b) To determine To find: The intercepts. Answer They- intercept is ( 0 , 1 ) and the x- intercept is ( 1 3 , 0 ) . Explanation Given information: The function is f ( x ) = x 2 − 3 x − 4 2 x 2 + x − 1 Calculation: Put x = 0 in function to find y-intercept. f ( 0 ) = 6 ( 0 ) 2 − 11 ( 0 ) + 3 6 ( 0 ) 2 − 7 ( 0 ) − 3 f ( 0 ) = − 1 Equate function to zero to find x intercept. f ( 0 ) = 0 ( 3 x − 1 ) ( 3 x + 1 ) = 0 3 x − 1 = 0 x = 1 3 Therefore, the y- intercept is ( 0 , 1 ) and the x- intercept is ( 1 3 , 0 ) . (c) To determine To find: The asymptotes. Answer The horizontal asymptote is y = 1 and vertical asymptote is x = 1 3 . Explanation Given information: The function is f ( x ) = x 2 − 3 x − 4 2 x 2 + x − 1 Calculation: In given function degree of numerator is same as degree of denominator. The horizontal asymptote will be the ratio of leading coefficient of numerator and denominator which is 3 3 = 1 . Equate denominator to zero to find vertical asymptote. 3 x + 1 = 0 x = 1 3 Therefore, the horizontal asymptote is y = 1 and vertical asymptote is x = 1 3 . (d) To determine To find: The sketch of graph. Answer The graph is shown in Figure-(1). Explanation Given information: The function is f ( x ) = x 2 − 3 x − 4 2 x 2 + x − 1 Calculation: The below table shows the value of y corresponding to the value of x . x − 2 − 1 1 3 f ( x ) 1.4 2 0.5 0.8 Draw the sketch for the function by using the equations of asymptotes. Figure-(1) Therefore, the graph is shown in Figure-(1).

3rd Edition

ISBN: 9781133947202

Author: Ron Larson

Publisher: Cengage Learning

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Question

Chapter 2.6, Problem 38E

(a)

To determine

To find:The domain of function.

(a)

Expert Solution

Answer to Problem 38E

The domain of function is all the real numbers except $x=32$ .

Explanation of Solution

Given information:

The function is $f(x)=x2−3x−42x2+x−1$

Calculation:

Consider the function.

. $f(x)=6x2−11x+36x2−7x−3$

Simplify the function.

$f(x)=6x2−11x+36x2−7x−3f(x)=(2x−3)(3x−1)(3x+1)(2x−3)f(x)=(3x−1)(3x+1)$

The function is valid for all the real numbers except $x=32$ and $x=−13$ .

Therefore, the domain of function is all the real numbers except $x=32$ and $x=−13$ .

(b)

To determine

To find:The intercepts.

(b)

Expert Solution

Answer to Problem 38E

They- intercept is $(0,1)$ and the x- intercept is $(13,0)$ .

Explanation of Solution

Given information:

The function is $f(x)=x2−3x−42x2+x−1$

Calculation:

Put $x=0$ in function to find y-intercept.

$f(0)=6(0)2−11(0)+36(0)2−7(0)−3f(0)=−1$

Equate function to zero to find x intercept.

$f(0)=0(3x−1)(3x+1)=03x−1=0x=13$

Therefore, the y- intercept is $(0,1)$ and the x- intercept is $(13,0)$ .

(c)

To determine

To find:The asymptotes.

(c)

Expert Solution

Answer to Problem 38E

The horizontal asymptote is $y=1$ and vertical asymptote is $x=13$ .

Explanation of Solution

Given information:

The function is $f(x)=x2−3x−42x2+x−1$

Calculation:

In given function degree of numerator is same as degree of denominator. The horizontal asymptote will be the ratio of leading coefficient of numerator and denominator which is $33=1$ .

Equate denominator to zero to find vertical asymptote.

$3x+1=0x=13$

Therefore, the horizontal asymptote is $y=1$ and vertical asymptote is $x=13$ .

(d)

To determine

To find:The sketch of graph.

(d)

Expert Solution

Answer to Problem 38E

The graph is shown in Figure-(1).

Explanation of Solution

Given information:

The function is $f(x)=x2−3x−42x2+x−1$

Calculation:

The below table shows the value of $y$ corresponding to the value of $x$ .

$x$	$−2$	$−1$	1	3
$f(x)$	1.4	2	0.5	0.8

Draw the sketch for the function by using the equations of asymptotes.

Precalculus with Limits, Chapter 2.6, Problem 38E

Figure-(1)

Therefore, the graph is shown in Figure-(1).

Chapter 2.6, Problem 37E

Chapter 2.6, Problem 39E

Chapter 2 Solutions

Precalculus with Limits

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Prob. 104E Ch. 2.5 - Prob. 105E Ch. 2.5 - Prob. 106E Ch. 2.5 - Prob. 107E Ch. 2.5 - Prob. 108E Ch. 2.5 - Prob. 109E Ch. 2.5 - Prob. 110E Ch. 2.5 - Prob. 111E Ch. 2.5 - Prob. 112E Ch. 2.5 - Prob. 113E Ch. 2.5 - Prob. 114E Ch. 2.5 - Prob. 115E Ch. 2.5 - Prob. 116E Ch. 2.5 - Prob. 117E Ch. 2.5 - Prob. 118E Ch. 2.5 - Prob. 119E Ch. 2.5 - Prob. 120E Ch. 2.5 - Prob. 121E Ch. 2.5 - Prob. 122E Ch. 2.5 - Prob. 123E Ch. 2.5 - Prob. 124E Ch. 2.5 - Prob. 125E Ch. 2.5 - Prob. 126E Ch. 2.5 - Prob. 127E Ch. 2.5 - Prob. 128E Ch. 2.5 - Prob. 129E Ch. 2.5 - Prob. 130E Ch. 2.5 - Prob. 131E Ch. 2.6 - Prob. 1E Ch. 2.6 - Prob. 2E Ch. 2.6 - Prob. 3E Ch. 2.6 - Prob. 4E Ch. 2.6 - Prob. 5E Ch. 2.6 - Prob. 6E Ch. 2.6 - Prob. 7E Ch. 2.6 - Prob. 8E Ch. 2.6 - Prob. 9E Ch. 2.6 - Prob. 10E Ch. 2.6 - Prob. 11E Ch. 2.6 - Prob. 12E Ch. 2.6 - Prob. 13E Ch. 2.6 - Prob. 14E Ch. 2.6 - Prob. 15E Ch. 2.6 - Prob. 16E Ch. 2.6 - Prob. 17E Ch. 2.6 - Prob. 18E Ch. 2.6 - Prob. 19E Ch. 2.6 - Prob. 20E Ch. 2.6 - Prob. 21E Ch. 2.6 - Prob. 22E Ch. 2.6 - Prob. 23E Ch. 2.6 - Prob. 24E Ch. 2.6 - Prob. 25E Ch. 2.6 - Prob. 26E Ch. 2.6 - Prob. 27E Ch. 2.6 - Prob. 28E Ch. 2.6 - Prob. 29E Ch. 2.6 - Prob. 30E Ch. 2.6 - Prob. 31E Ch. 2.6 - Prob. 32E Ch. 2.6 - Prob. 33E Ch. 2.6 - Prob. 34E Ch. 2.6 - Prob. 35E Ch. 2.6 - Prob. 36E Ch. 2.6 - Prob. 37E Ch. 2.6 - Prob. 38E Ch. 2.6 - Prob. 39E Ch. 2.6 - Prob. 40E Ch. 2.6 - Prob. 41E Ch. 2.6 - Prob. 42E Ch. 2.6 - Prob. 43E Ch. 2.6 - Prob. 44E Ch. 2.6 - Prob. 45E Ch. 2.6 - Prob. 46E Ch. 2.6 - Prob. 47E Ch. 2.6 - Prob. 48E Ch. 2.6 - Prob. 49E Ch. 2.6 - Prob. 50E Ch. 2.6 - Prob. 51E Ch. 2.6 - Prob. 52E Ch. 2.6 - Prob. 53E Ch. 2.6 - Prob. 54E Ch. 2.6 - Prob. 55E Ch. 2.6 - Prob. 56E Ch. 2.6 - Prob. 57E Ch. 2.6 - Prob. 58E Ch. 2.6 - Prob. 59E Ch. 2.6 - Prob. 60E Ch. 2.6 - Prob. 61E Ch. 2.6 - Prob. 62E Ch. 2.6 - Prob. 63E Ch. 2.6 - Prob. 64E Ch. 2.6 - Prob. 65E Ch. 2.6 - Prob. 66E Ch. 2.6 - Prob. 67E Ch. 2.6 - Prob. 68E Ch. 2.6 - Prob. 69E Ch. 2.6 - Prob. 70E Ch. 2.6 - Prob. 71E Ch. 2.6 - Prob. 72E Ch. 2.6 - Prob. 73E Ch. 2.6 - Prob. 74E Ch. 2.6 - Prob. 75E Ch. 2.6 - Prob. 76E Ch. 2.6 - Prob. 77E Ch. 2.6 - Prob. 78E Ch. 2.6 - Prob. 79E Ch. 2.6 - Prob. 80E Ch. 2.6 - Prob. 81E Ch. 2.6 - Prob. 82E Ch. 2.7 - Prob. 1E Ch. 2.7 - Prob. 2E Ch. 2.7 - Prob. 3E Ch. 2.7 - Prob. 4E Ch. 2.7 - Prob. 5E Ch. 2.7 - Prob. 6E Ch. 2.7 - Prob. 7E Ch. 2.7 - Prob. 8E Ch. 2.7 - Prob. 9E Ch. 2.7 - Prob. 10E Ch. 2.7 - Prob. 11E Ch. 2.7 - Prob. 12E Ch. 2.7 - Prob. 13E Ch. 2.7 - Prob. 14E Ch. 2.7 - Prob. 15E Ch. 2.7 - Prob. 16E Ch. 2.7 - Prob. 17E Ch. 2.7 - Prob. 18E Ch. 2.7 - Prob. 19E Ch. 2.7 - Prob. 20E Ch. 2.7 - Prob. 21E Ch. 2.7 - Prob. 22E Ch. 2.7 - Prob. 23E Ch. 2.7 - Prob. 24E Ch. 2.7 - Prob. 25E Ch. 2.7 - Prob. 26E Ch. 2.7 - Prob. 27E Ch. 2.7 - Prob. 28E Ch. 2.7 - Prob. 29E Ch. 2.7 - Prob. 30E Ch. 2.7 - Prob. 31E Ch. 2.7 - Prob. 32E Ch. 2.7 - Prob. 33E Ch. 2.7 - Prob. 34E Ch. 2.7 - Prob. 35E Ch. 2.7 - Prob. 36E Ch. 2.7 - Prob. 37E Ch. 2.7 - Prob. 38E Ch. 2.7 - Prob. 39E Ch. 2.7 - Prob. 40E Ch. 2.7 - Prob. 41E Ch. 2.7 - Prob. 42E Ch. 2.7 - Prob. 43E Ch. 2.7 - Prob. 44E Ch. 2.7 - Prob. 45E Ch. 2.7 - Prob. 46E Ch. 2.7 - Prob. 47E Ch. 2.7 - Prob. 48E Ch. 2.7 - Prob. 49E Ch. 2.7 - Prob. 50E Ch. 2.7 - Prob. 51E Ch. 2.7 - Prob. 52E Ch. 2.7 - Prob. 53E Ch. 2.7 - Prob. 54E Ch. 2.7 - Prob. 55E Ch. 2.7 - Prob. 56E Ch. 2.7 - Prob. 57E Ch. 2.7 - Prob. 58E Ch. 2.7 - Prob. 59E Ch. 2.7 - Prob. 60E Ch. 2.7 - Prob. 61E Ch. 2.7 - Prob. 62E Ch. 2.7 - Prob. 63E Ch. 2.7 - Prob. 64E Ch. 2.7 - Prob. 65E Ch. 2.7 - Prob. 66E Ch. 2.7 - Prob. 67E Ch. 2.7 - Prob. 68E Ch. 2.7 - Prob. 69E Ch. 2.7 - Prob. 70E Ch. 2.7 - Prob. 71E Ch. 2.7 - Prob. 72E Ch. 2.7 - Prob. 73E Ch. 2.7 - Prob. 74E Ch. 2.7 - Prob. 75E Ch. 2.7 - Prob. 76E Ch. 2.7 - Prob. 77E Ch. 2.7 - Prob. 78E Ch. 2.7 - Prob. 79E Ch. 2.7 - Prob. 80E Ch. 2.7 - Prob. 81E Ch. 2.7 - Prob. 82E Ch. 2.7 - Prob. 83E Ch. 2.7 - Prob. 84E Ch. 2.7 - Prob. 85E Ch. 2.7 - Prob. 86E Ch. 2.7 - Prob. 87E Ch. 2.7 - Prob. 88E Ch. 2.7 - Prob. 89E Ch. 2.7 - Prob. 90E Ch. 2 - Prob. 1RE Ch. 2 - Prob. 2RE Ch. 2 - Prob. 3RE Ch. 2 - Prob. 4RE Ch. 2 - Prob. 5RE Ch. 2 - Prob. 6RE Ch. 2 - Prob. 7RE Ch. 2 - Prob. 8RE Ch. 2 - Prob. 9RE Ch. 2 - Prob. 10RE Ch. 2 - Prob. 11RE Ch. 2 - Prob. 12RE Ch. 2 - Prob. 13RE Ch. 2 - Prob. 14RE Ch. 2 - Prob. 15RE Ch. 2 - Prob. 16RE Ch. 2 - Prob. 17RE Ch. 2 - Prob. 18RE Ch. 2 - Prob. 19RE Ch. 2 - Prob. 20RE Ch. 2 - Prob. 21RE Ch. 2 - Prob. 22RE Ch. 2 - Prob. 23RE Ch. 2 - Prob. 24RE Ch. 2 - Prob. 25RE Ch. 2 - Prob. 26RE Ch. 2 - Prob. 27RE Ch. 2 - Prob. 28RE Ch. 2 - Prob. 29RE Ch. 2 - Prob. 30RE Ch. 2 - Prob. 31RE Ch. 2 - Prob. 32RE Ch. 2 - Prob. 33RE Ch. 2 - Prob. 34RE Ch. 2 - Prob. 35RE Ch. 2 - Prob. 36RE Ch. 2 - Prob. 37RE Ch. 2 - Prob. 38RE Ch. 2 - Prob. 39RE Ch. 2 - Prob. 40RE Ch. 2 - Prob. 41RE Ch. 2 - Prob. 42RE Ch. 2 - Prob. 43RE Ch. 2 - Prob. 44RE Ch. 2 - Prob. 45RE Ch. 2 - Prob. 46RE Ch. 2 - Prob. 47RE Ch. 2 - Prob. 48RE Ch. 2 - Prob. 49RE Ch. 2 - Prob. 50RE Ch. 2 - Prob. 51RE Ch. 2 - Prob. 52RE Ch. 2 - Prob. 53RE Ch. 2 - Prob. 54RE Ch. 2 - Prob. 55RE Ch. 2 - Prob. 56RE Ch. 2 - Prob. 57RE Ch. 2 - Prob. 58RE Ch. 2 - Prob. 59RE Ch. 2 - Prob. 60RE Ch. 2 - Prob. 61RE Ch. 2 - Prob. 62RE Ch. 2 - Prob. 63RE Ch. 2 - Prob. 64RE Ch. 2 - Prob. 65RE Ch. 2 - Prob. 66RE Ch. 2 - Prob. 1CT Ch. 2 - Prob. 2CT Ch. 2 - Prob. 3CT Ch. 2 - Prob. 4CT Ch. 2 - Prob. 5CT Ch. 2 - Prob. 6CT Ch. 2 - Prob. 7CT Ch. 2 - Prob. 8CT Ch. 2 - Prob. 9CT Ch. 2 - Prob. 10CT Ch. 2 - Prob. 11CT Ch. 2 - Prob. 12CT Ch. 2 - Prob. 13CT Ch. 2 - Prob. 14CT Ch. 2 - Prob. 15CT Ch. 2 - Prob. 16CT Ch. 2 - Prob. 17CT Ch. 2 - Prob. 18CT Ch. 2 - Prob. 1PS Ch. 2 - Prob. 2PS Ch. 2 - Prob. 3PS Ch. 2 - Prob. 4PS Ch. 2 - Prob. 5PS Ch. 2 - Prob. 6PS Ch. 2 - Prob. 7PS Ch. 2 - Prob. 8PS Ch. 2 - Prob. 9PS Ch. 2 - Prob. 10PS Ch. 2 - Prob. 11PS Ch. 2 - Prob. 12PS Ch. 2 - Prob. 13PS

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