Explanation Definition used: Vertical Asymptote : “A vertical asymptote occurs in the graph of f ( x ) = P ( x ) Q ( x ) at those values of x where Q ( x ) = 0 and P ( x ) ≠ 0 . That is, at values of x where the denominator equals 0 but the numerator does not equal 0”. Slant asymptote : If f ( x ) = n ( x ) d ( x ) is a rational function for which the degree of n ( x ) is 1 more than the degree of d ( x ) , then use polynomial long division method to write f ( x ) = m x + b + r ( x ) d ( x ) , where the degree of r ( x ) is less than the degree of d ( x ) . The line y = m x + b is an oblique or slant asymptote for the graph of y = f ( x ) . Result used: Determine the Horizontal asymptotes of a Rational Function : “Consider the rational function f ( x ) = P ( x ) Q ( x ) = a n x n + ... + a 1 x + a 0 b m x m + ... + b 1 x + b 0 , a n ≠ 0 and b m ≠ 0 . 1. If n < m , a horizontal asymptote occurs at y = 0 (the x -axis). 2. If n = m , a horizontal asymptote occurs at y = a n b m . 3. If n > m , there is no horizontal asymptote.” Description: The given function is f ( x ) = x 3 − 1 x 2 − 9 . Obtain the vertical asymptote as follows. To find the vertical asymptote of the function f ( x ) = x 3 − 1 x 2 − 9 ; equate the denominator of f ( x ) to zero. x 2 − 9 = 0 x 2 = 9 x = − 3 or x = 3 That is, the denominator is zero when x = − 3 and x = 3 and the numerator is not zero at x = − 3 or x = 3

College Algebra in Context, Books a la Carte Edition plus MyLab Math with Pearson eText -- Access Card Package (5th Edition)

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ISBN: 9780134397016

Author: Ronald J. Harshbarger, Lisa S. Yocco

Publisher: PEARSON

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Chapter 6.5, Problem 24E

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To find: The equation of vertical, horizontal and slant asymptotes of the function f(x)=x3−1x2−9 and sketch the graph of the function.

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Chapter 6.5, Problem 23E

Chapter 6.5, Problem 25E

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College Algebra in Context, Books a la Carte Edition plus MyLab Math with Pearson eText -- Access Card Package (5th Edition)

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Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - For Exercises 1116, match the polynomial function...Ch. 6.1 - For Exercises 1720, use the equation of the...Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Sketch a graph of any cubic polynomial function...Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Daily Revenue The daily revenue in dollars from...Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Starbucks Using data from 2005 and projected to...Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Salaries The median salary for male workers, in...Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.2 - Find the cubic function that models the data in...Ch. 6.2 - Find the cubic function that is the best fit for...Ch. 6.2 - Prob. 3E Ch. 6.2 - Find the quartic function that is the best fit for...Ch. 6.2 - Prob. 5E Ch. 6.2 - a. 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Prob. 18E Ch. 6.6 - Prob. 19E Ch. 6.6 - Prob. 20E Ch. 6.6 - Prob. 21E Ch. 6.6 - Prob. 22E Ch. 6.6 - Prob. 23E Ch. 6.6 - Prob. 24E Ch. 6.6 - Prob. 25E Ch. 6.6 - Combine factoring with graphical and/or numerical...Ch. 6.6 - Prob. 27E Ch. 6.6 - 28. Average Cost The average cost per set for the...Ch. 6.6 - Prob. 29E Ch. 6.6 - Prob. 30E Ch. 6.6 - Prob. 31E Ch. 6.6 - Prob. 32E Ch. 6.6 - Prob. 33E Ch. 6.6 - Prob. 34E Ch. 6.6 - Population Suppose the number of employees of a...Ch. 6 - For Exercises 14, (a) give the degree of the...Ch. 6 - For Exercises 14, (a) give the degree of the...Ch. 6 - Prob. 3TE Ch. 6 - Prob. 4TE Ch. 6 - Prob. 5TE Ch. 6 - Prob. 6TE Ch. 6 - Prob. 7TE Ch. 6 - Prob. 8TE Ch. 6 - Prob. 9TE Ch. 6 - Prob. 10TE Ch. 6 - Prob. 11TE Ch. 6 - Prob. 12TE Ch. 6 - Prob. 13TE Ch. 6 - Prob. 14TE Ch. 6 - In Exercises 1116, simplify each rational...Ch. 6 - Prob. 16TE Ch. 6 - Prob. 17TE Ch. 6 - Prob. 18TE Ch. 6 - Prob. 19TE Ch. 6 - Prob. 20TE Ch. 6 - Prob. 21TE Ch. 6 - Prob. 22TE Ch. 6 - Prob. 23TE Ch. 6 - Prob. 24TE Ch. 6 - Prob. 25TE Ch. 6 - Prob. 26TE Ch. 6 - Prob. 27TE Ch. 6 - Prob. 28TE Ch. 6 - Prob. 29TE Ch. 6 - Prob. 30TE Ch. 6 - Prob. 31TE Ch. 6 - Prob. 32TE Ch. 6 - Prob. 33TE Ch. 6 - Prob. 34TE Ch. 6 - Prob. 35TE Ch. 6 - Prob. 36TE Ch. 6 - Prob. 37TE Ch. 6 - Prob. 38TE Ch. 6 - Prob. 39TE Ch. 6 - Prob. 40TE Ch. 6 - In Exercises 3841, perform the long division. 41....Ch. 6 - Prob. 1RE Ch. 6 - Prob. 2RE Ch. 6 - Prob. 3RE Ch. 6 - Prob. 4RE Ch. 6 - Prob. 5RE Ch. 6 - Prob. 6RE Ch. 6 - Prob. 7RE Ch. 6 - Prob. 8RE Ch. 6 - Solve x4 x3 20x2 = 0.Ch. 6 - Prob. 10RE Ch. 6 - Prob. 11RE Ch. 6 - Prob. 12RE Ch. 6 - Prob. 13RE Ch. 6 - Prob. 14RE Ch. 6 - Prob. 15RE Ch. 6 - Prob. 16RE Ch. 6 - Prob. 17RE Ch. 6 - Prob. 18RE Ch. 6 - Find one solution of 3x3 x2 12x + 4 = 0...Ch. 6 - Find one solution of 2x3 + 5x2 4x 3 = 0...Ch. 6 - Prob. 21RE Ch. 6 - Prob. 22RE Ch. 6 - Prob. 23RE Ch. 6 - Prob. 24RE Ch. 6 - Prob. 25RE Ch. 6 - Prob. 26RE Ch. 6 - Prob. 27RE Ch. 6 - Prob. 28RE Ch. 6 - Prob. 29RE Ch. 6 - Prob. 30RE Ch. 6 - Prob. 31RE Ch. 6 - Prob. 32RE Ch. 6 - Prob. 33RE Ch. 6 - Revenue The monthly revenue for a product is given...Ch. 6 - Prob. 35RE Ch. 6 - Prob. 36RE Ch. 6 - Prob. 37RE Ch. 6 - Prob. 38RE Ch. 6 - Foreign Born Population The table on the following...Ch. 6 - Prob. 40RE Ch. 6 - Prob. 41RE Ch. 6 - Break-Even The daily profit in dollars for a...Ch. 6 - Starbucks The table gives the total number of...Ch. 6 - Drugs in the Bloodstream The concentration of a...Ch. 6 - Prob. 45RE Ch. 6 - Prob. 46RE Ch. 6 - Prob. 47RE Ch. 6 - Prob. 48RE Ch. 6 - Prob. 49RE Ch. 6 - Prob. 50RE Ch. 6 - Prob. 51RE Ch. 6 - Prob. 52RE Ch. 6 - Prob. 53RE Ch. 6 - Cost-Benefit The percent p of particulate...

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The equation of vertical, horizontal and slant asymptotes of the function f ( x ) = x 3 − 1 x 2 − 9 and sketch the graph of the function.

Solution Summary: The author analyzes the vertical, horizontal, and slant asymptotes of a rational function.

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To find: The equation of vertical, horizontal and slant asymptotes of the function f(x)=x3−1x2−9 and sketch the graph of the function.

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Chapter 6 Solutions