a. Answer R − { − 0.5 , 0.5 } Explanation Given: Function: f ( x ) = 6 x 2 − 7 x + 2 4 x 2 − 1 Concept used: The domain of the function is the set of values, where the function is defined. Calculation: Now, finding the domain of the function, When x = − 0.5 , x = 0.5 , the function is undefined. So, the domain of the function is R − { − 0.5 , 0.5 } . Conclusion: Hence, the domain of the function is R − { − 0.5 , 0.5 } . . b. To determine To find the intercepts of the function f ( x ) = 6 x 2 − 7 x + 2 4 x 2 − 1 . Answer (0.333, 0), (0, -1) Explanation Given: Function: f ( x ) = 6 x 2 − 7 x + 2 4 x 2 − 1 Calculation: Consider the function f ( x ) = 6 x 2 − 7 x + 2 4 x 2 − 1 , ⇒ f ( x ) = 6 x 2 − 7 x + 2 4 x 2 − 1 ⇒ f ( x ) = 6 x 2 − 3 x − 4 x + 2 ( 2 x ) 2 − 1 2 ⇒ f ( x ) = 3 x ( 2 x − 1 ) − 1 ( 2 x − 1 ) ( 2 x − 1 ) ( 2 x + 1 ) ⇒ f ( x ) = ( 2 x − 1 ) ( 3 x − 1 ) ( 2 x − 1 ) ( 2 x + 1 ) ⇒ f ( x ) = 3 x − 1 2 x + 1 To find the y-intercept, put x = 0 in given function. ⇒ f ( 0 ) = 3 ( 0 ) − 1 2 ( 0 ) + 1 = − 1 1 = − 1 So, y-intercept is (0, -1). To find the x-intercept, put f ( x ) = y = 0 in given function. ⇒ 0 = 3 x − 1 2 x + 1 ⇒ 0 = 3 x − 1 ⇒ 3 x = 1 ⇒ x = 1 3 = 0.333 So, the x- intercept is (0.333, 0). Conclusion: Therefore, the x-intercept is (0.333, 0) and y-intercept is (0, -1). c. To determine To find the asymptotes to the function f ( x ) = 6 x 2 − 7 x + 2 4 x 2 − 1 . Answer x = − 0.5 , y = 1.5 Explanation Given: Function: f ( x ) = 6 x 2 − 7 x + 2 4 x 2 − 1 Calculation: ⇒ f ( x ) = 6 x 2 − 7 x + 2 4 x 2 − 1 ⇒ f ( x ) = 6 x 2 − 3 x − 4 x + 2 ( 2 x ) 2 − 1 2 ⇒ f ( x ) = 3 x ( 2 x − 1 ) − 1 ( 2 x − 1 ) ( 2 x − 1 ) ( 2 x + 1 ) ⇒ f ( x ) = ( 2 x − 1 ) ( 3 x − 1 ) ( 2 x − 1 ) ( 2 x + 1 ) ⇒ f ( x ) = 3 x − 1 2 x + 1 Asymptotes: Vertical asymptotes: To find vertical asymptotes, put denominator of the given function equal to zero. ⇒ 2 x + 1 = 0 ⇒ 2 x = − 1 ⇒ x = − 1 2 = − 0.5 Horizontal asymptotes: As the degree of numerator is equal to the degree of the denominator, the horizontal asymptote for given function is ⇒ y = leading coefficient of numerator leading coefficient of denominator ⇒ y = 3 2 ⇒ y = 1.5 Conclusion: Therefore, the vertical asymptote is x = − 0.5 and horizontal asymptote is y = 1.5. d. To determine To sketch the function f ( x ) = 6 x 2 − 7 x + 2 4 x 2 − 1 . Explanation Given: Function: f ( x ) = 6 x 2 − 7 x + 2 4 x 2 − 1 Calculation for graph: Consider f ( x ) = 6 x 2 − 7 x + 2 4 x 2 − 1 Values of x Values of h(x) 0 -2 1 0.333 -1 5 2 0.8 -2 2.666 By taking different values of x, the graph can be plotted. Graph: Interpretation: The above graph represents the sketch of given function.

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 2, Problem 56RE

To determine

To calculate the domain of the function f(x)=6x2−7x+24x2−1 .

Expert Solution

Answer to Problem 56RE

R−{−0.5,0.5}

Explanation of Solution

Given:

Function: f(x)=6x2−7x+24x2−1

Concept used:

The domain of the function is the set of values, where the function is defined.

Calculation:

Now, finding the domain of the function,

When x=−0.5,x=0.5 , the function is undefined.

So, the domain of the function is R−{−0.5,0.5}.

Conclusion:

Hence, the domain of the function is R−{−0.5,0.5}. .

To determine

To find the intercepts of the function f(x)=6x2−7x+24x2−1 .

Expert Solution

Answer to Problem 56RE

(0.333, 0), (0, -1)

Explanation of Solution

Given:

Function: f(x)=6x2−7x+24x2−1

Calculation:

Consider the function f(x)=6x2−7x+24x2−1 ,

⇒f(x)=6x2−7x+24x2−1⇒f(x)=6x2−3x−4x+2(2x)2−12⇒f(x)=3x(2x−1)−1(2x−1)(2x−1)(2x+1)⇒f(x)=(2x−1)(3x−1)(2x−1)(2x+1)⇒f(x)=3x−12x+1

To find the y-intercept, put x=0 in given function.

⇒f(0)=3(0)−12(0)+1=−11=−1

So, y-intercept is (0, -1).

To find the x-intercept, put f(x)=y=0 in given function.

⇒0=3x−12x+1⇒0=3x−1⇒3x=1⇒x=13=0.333

So, the x- intercept is (0.333, 0).

Conclusion:

Therefore, the x-intercept is (0.333, 0) and y-intercept is (0, -1).

To determine

To find the asymptotes to the function f(x)=6x2−7x+24x2−1 .

Expert Solution

Answer to Problem 56RE

x=−0.5,y=1.5

Explanation of Solution

Given:

Function: f(x)=6x2−7x+24x2−1

Calculation:

⇒f(x)=6x2−7x+24x2−1⇒f(x)=6x2−3x−4x+2(2x)2−12⇒f(x)=3x(2x−1)−1(2x−1)(2x−1)(2x+1)⇒f(x)=(2x−1)(3x−1)(2x−1)(2x+1)⇒f(x)=3x−12x+1

Asymptotes:

Vertical asymptotes:

To find vertical asymptotes, put denominator of the given function equal to zero.

⇒2x+1=0⇒2x=−1⇒x=−12=−0.5

Horizontal asymptotes:

As the degree of numerator is equal to the degree of the denominator, the horizontal asymptote for given function is

⇒y=leading coefficient of numeratorleading coefficient of denominator⇒y=32⇒y=1.5

Conclusion:

Therefore, the vertical asymptote is x=−0.5 and horizontal asymptote is y = 1.5.

To determine

To sketch the function f(x)=6x2−7x+24x2−1 .

Expert Solution

Explanation of Solution

Given:

Function: f(x)=6x2−7x+24x2−1

Calculation for graph:

Consider f(x)=6x2−7x+24x2−1

Values of x	Values of h(x)
0	-2
1	0.333
-1	5
2	0.8
-2	2.666

By taking different values of x, the graph can be plotted.

Graph:

EBK PRECALCULUS W/LIMITS, Chapter 2, Problem 56RE

Interpretation:

The above graph represents the sketch of given function.

Chapter 2, Problem 55RE

Chapter 2, Problem 57RE

Chapter 2 Solutions

EBK PRECALCULUS W/LIMITS

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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. 67RE Ch. 2 - Prob. 68RE 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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Asymptotes - What are they? : ExamSolutions Maths Revision; Author: ExamSolutions;https://www.youtube.com/watch?v=5Hl_WJXcR6M;License: Standard YouTube License, CC-BY

To calculate the domain of the function f ( x ) = 6 x 2 − 7 x + 2 4 x 2 − 1 .

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To calculate the domain of the function f(x)=6x2−7x+24x2−1 .

Answer to Problem 56RE

Explanation of Solution

To find the intercepts of the function f(x)=6x2−7x+24x2−1 .

Answer to Problem 56RE

Explanation of Solution

To find the asymptotes to the function f(x)=6x2−7x+24x2−1 .

Answer to Problem 56RE

Explanation of Solution

To sketch the function f(x)=6x2−7x+24x2−1 .

Explanation of Solution

Chapter 2 Solutions