(a) Answer The power function end behavior model for f ( x ) = 4 x 3 − 2 x + 1 x − 2 is 4 x 2 . Explanation Given information: The function is f ( x ) = 4 x 3 − 2 x + 1 x − 2 . Calculation: The power functionend behavior model of a polynomial function is the highest power term. The given function f ( x ) = 4 x 3 − 2 x + 1 x − 2 is a polynomial function.The power function end behavior model for numerator of the function is 4 x 3 and the denominatoris x . So, the power function end behavior model of f ( x ) = 4 x 3 − 2 x + 1 x − 2 is: 4 x 3 x = 4 x 2 Therefore, the power function end behavior model for f ( x ) = 4 x 3 − 2 x + 1 x − 2 is 4 x 2 . (b) To determine To find: The horizontal asymptote of function f ( x ) = 4 x 3 − 2 x + 1 x − 2 . Answer There is no horizontal asymptote of the function f ( x ) = 4 x 3 − 2 x + 1 x − 2 . Explanation Given information: The given function is f ( x ) = 4 x 3 − 2 x + 1 x − 2 . Calculation: The horizontal asymptote of the function f ( x ) = 4 x 3 − 2 x + 1 x − 2 is y = lim x → ∞ ( 4 x 2 ) , for a finite value. To graph a function y = 4 x 2 , follow the steps using graphing calculator. First press “ON” button on graphical calculator, press Y = key and enter right hand side of the equation y = 4 x 2 after the symbol Y 1 . Enter the keystrokes 4 X ^ 2 . The display will show the equation, Y 1 = 4 X ^ 2 Now, press the GRAPH key and TRACE key to produce the graph of given function in standard window as shown below. Figure (1) As observed from graph of function g ( x ) = 4 x 2 tends to ∞ as x to ∞ . Therefore, there is no horizontal asymptote for f ( x ) = 4 x 3 − 2 x + 1 x − 2 .

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 2.2, Problem 43E

(a)

To determine

To find: The power function end behavior model for f(x)=4x3−2x+1x−2 .

(a)

Expert Solution

Answer to Problem 43E

The power function end behavior model for f(x)=4x3−2x+1x−2 is 4x2 .

Explanation of Solution

Given information:

The function is f(x)=4x3−2x+1x−2 .

Calculation:

The power functionend behavior model of a polynomial function is the highest power term.

The given function f(x)=4x3−2x+1x−2 is a polynomial function.The power function end behavior model for numerator of the function is 4x3 and the denominatoris x .

So, the power function end behavior model of f(x)=4x3−2x+1x−2 is:

4x3x=4x2

Therefore, the power function end behavior model for f(x)=4x3−2x+1x−2 is 4x2 .

(b)

To determine

To find:The horizontal asymptote of function f(x)=4x3−2x+1x−2 .

(b)

Expert Solution

Answer to Problem 43E

There is no horizontal asymptote of the function f(x)=4x3−2x+1x−2 .

Explanation of Solution

Given information:

The given function is f(x)=4x3−2x+1x−2 .

Calculation:

The horizontal asymptote of the function f(x)=4x3−2x+1x−2 is y=limx→∞(4x2) , for a finite value.

To graph a function y=4x2 , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press Y= key and enter right hand side of the equation y=4x2 after the symbol Y1 . Enter the keystrokes 4X^2 .

The display will show the equation,

Y1=4X^2

Now, press the GRAPH key and TRACE key to produce the graph of given function in standard window as shown below.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 2.2, Problem 43E

Figure (1)

As observed from graph of function g(x)=4x2 tends to ∞ as x to ∞ .

Therefore, there is no horizontal asymptote for f(x)=4x3−2x+1x−2 .

Chapter 2.2, Problem 42E

Chapter 2.2, Problem 44E

Chapter 2 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 2.1 - Prob. 1QR Ch. 2.1 - Prob. 2QR Ch. 2.1 - Prob. 3QR Ch. 2.1 - Prob. 4QR Ch. 2.1 - Prob. 5QR Ch. 2.1 - Prob. 6QR Ch. 2.1 - Prob. 7QR Ch. 2.1 - Prob. 8QR Ch. 2.1 - Prob. 9QR Ch. 2.1 - Prob. 10QR

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Prob. 1QQ Ch. 2.4 - Prob. 2QQ Ch. 2.4 - Prob. 3QQ Ch. 2.4 - Prob. 4QQ 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

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The power function end behavior model for f ( x ) = 4 x 3 − 2 x + 1 x − 2 .

Concept explainers

Videos

To find: The power function end behavior model for f(x)=4x3−2x+1x−2 .

Answer to Problem 43E

Explanation of Solution

To find:The horizontal asymptote of function f(x)=4x3−2x+1x−2 .

Answer to Problem 43E

Explanation of Solution

Chapter 2 Solutions

Additional Math Textbook Solutions