(a) Answer The power function end behavior model for f ( x ) = x − 2 2 x 2 + 3 x − 5 is 1 2 x . Explanation Given information: The function is f ( x ) = x − 2 2 x 2 + 3 x − 5 . Calculation: The power function end behavior model of a polynomial function is the highest power term.The given function f ( x ) = x − 2 2 x 2 + 3 x − 5 is a polynomial function. The power function end behavior model of the numerator of the function is x and denominator of the functionis 2 x 2 .So, the power function end behavior model of the function is: x 2 x 2 = 1 2 x Therefore, the power function end behavior model for f ( x ) = x − 2 2 x 2 + 3 x − 5 is 1 2 x . (b) To determine To find: The horizontal asymptote of function f ( x ) = x − 2 2 x 2 + 3 x − 5 . Answer The horizontal asymptote of function f ( x ) = x − 2 2 x 2 + 3 x − 5 is y = 0 . Explanation Given information: The given function is f ( x ) = x − 2 2 x 2 + 3 x − 5 . Calculation: The horizontal asymptote of the function f ( x ) = x − 2 2 x 2 + 3 x − 5 is y = lim x → ∞ ( 1 2 x ) , for a finite value. To graph a function y = 1 2 x , 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 = 1 2 x after the symbol Y 1 . Enter the keystrokes 1 ÷ ( 2 X ) . The display will show the equation, Y 1 = 1 / ( 2 X ) 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 ) = 1 2 x tends to 0 as x to ∞ . Therefore, the horizontal asymptote of function f ( x ) = x − 2 2 x 2 + 3 x − 5 is y = 0 .

Calculus: Graphical, Numerical, Algebraic: Solutions Manual

3rd Edition

ISBN: 9780132014144

Author: Ross L. Finney, Franklin Demana, Bert K. Waits, Daniel Kennedy

Publisher: Pearson Prentice Hall

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Question

Chapter 2.2, Problem 41E

(a)

To determine

To find: The power function end behavior model for f(x)=x−22x2+3x−5 .

(a)

Expert Solution

Answer to Problem 41E

The power function end behavior model for f(x)=x−22x2+3x−5 is 12x .

Explanation of Solution

Given information:

The function is f(x)=x−22x2+3x−5 .

Calculation:

The power function end behavior model of a polynomial function is the highest power term.The given function f(x)=x−22x2+3x−5 is a polynomial function.

The power function end behavior model of the numerator of the function is x and denominator of the functionis 2x2 .So, the power function end behavior model of the function is:

x2x2=12x

Therefore, the power function end behavior model for f(x)=x−22x2+3x−5 is 12x .

(b)

To determine

To find:The horizontal asymptote of function f(x)=x−22x2+3x−5 .

(b)

Expert Solution

Answer to Problem 41E

The horizontal asymptote of function f(x)=x−22x2+3x−5 is y=0 .

Explanation of Solution

Given information:

The given function is f(x)=x−22x2+3x−5 .

Calculation:

The horizontal asymptote of the function f(x)=x−22x2+3x−5 is y=limx→∞(12x) , for a finite value.

To graph a function y=12x , 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=12x after the symbol Y1 . Enter the keystrokes 1÷(2X) .

The display will show the equation,

Y1=1/(2X)

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

Calculus: Graphical, Numerical, Algebraic: Solutions Manual, Chapter 2.2, Problem 41E

Figure (1)

As observed from graph of function g(x)=12x tends to 0 as x to ∞ .

Therefore, the horizontal asymptote of function f(x)=x−22x2+3x−5 is y=0 .

Chapter 2.2, Problem 40E

Chapter 2.2, Problem 42E

Chapter 2 Solutions

Calculus: Graphical, Numerical, Algebraic: Solutions Manual

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

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 49E Ch. 2.1 - Prob. 50E Ch. 2.1 - 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Prob. 5E Ch. 2.4 - Prob. 6E Ch. 2.4 - Prob. 7E Ch. 2.4 - Prob. 8E Ch. 2.4 - Prob. 9E Ch. 2.4 - Prob. 10E Ch. 2.4 - Prob. 11E Ch. 2.4 - Prob. 12E Ch. 2.4 - Prob. 13E Ch. 2.4 - Prob. 14E Ch. 2.4 - Prob. 15E Ch. 2.4 - Prob. 16E Ch. 2.4 - Prob. 17E Ch. 2.4 - Prob. 18E Ch. 2.4 - Prob. 19E Ch. 2.4 - Prob. 20E Ch. 2.4 - Prob. 21E Ch. 2.4 - Prob. 22E Ch. 2.4 - Prob. 23E Ch. 2.4 - Prob. 24E Ch. 2.4 - Prob. 25E Ch. 2.4 - Prob. 26E Ch. 2.4 - Prob. 27E Ch. 2.4 - Prob. 28E Ch. 2.4 - Prob. 29E Ch. 2.4 - Prob. 30E Ch. 2.4 - Prob. 31E Ch. 2.4 - Prob. 32E Ch. 2.4 - Prob. 33E Ch. 2.4 - Prob. 34E Ch. 2.4 - Prob. 35E Ch. 2.4 - Prob. 36E Ch. 2.4 - Prob. 37E Ch. 2.4 - Prob. 38E Ch. 2.4 - Prob. 39E Ch. 2.4 - Prob. 40E Ch. 2.4 - Prob. 41E Ch. 2.4 - Prob. 42E Ch. 2.4 - Prob. 43E Ch. 2.4 - Prob. 44E Ch. 2.4 - Prob. 45E Ch. 2.4 - Prob. 46E Ch. 2.4 - Prob. 47E Ch. 2.4 - Prob. 48E Ch. 2.4 - Prob. 49E Ch. 2.4 - Prob. 50E Ch. 2.4 - Prob. 51E Ch. 2.4 - Prob. 52E Ch. 2.4 - Prob. 53E Ch. 2.4 - Prob. 54E Ch. 2.4 - Prob. 55E Ch. 2.4 - 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 ) = x − 2 2 x 2 + 3 x − 5 .

Concept explainers

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To find: The power function end behavior model for f(x)=x−22x2+3x−5 .

Answer to Problem 41E

Explanation of Solution

To find:The horizontal asymptote of function f(x)=x−22x2+3x−5 .

Answer to Problem 41E

Explanation of Solution

Chapter 2 Solutions

Additional Math Textbook Solutions