Explanation Concept: a) Domain of the function is set of all the possible values where the given function is defined. b) For any rational function f ( x ) = p ( x ) q ( x ) , where p ( x ) and q ( x ) are polynomial with no common factors other than constants, if α is a zero of the denominator, then the line x = α is a vertical asymptote for the graph of the function. c) If the degree of the numerator and denominator in a rational function is same, horizontal asymptote is given by y = a b , where a and b is the leading coefficients of numerator and denominator respectively. d) For any rational function f ( x ) = p ( x ) q ( x ) , if the degree of p ( x ) is less than q ( x ) then horizontal asymptotes are given by y = 0 or x -axis. e) For any rational function f ( x ) = p ( x ) q ( x ) , if the degree of p ( x ) is greater than q ( x ) then, there will be no horizontal asymptotes. f) In a rational function f ( x ) = p ( x ) q ( x ) , the degree of p ( x ) is greater than q ( x ) by one degree, then the asymptotes obtained are called oblique asymptotes. Factorize the function f ( x ) . f ( x ) = x 3 − 4 x x 2 − x = x ( x 2 − 4 ) x ( x − 1 ) = x ( x − 2 ) ( x + 2 ) x ( x − 1 ) a) The zero of the denominator of f ( x ) are 0 and 1 , then the domain of the function is ( − ∞ , 0 ) ∪ ( 0 , 1 ) ∪ ( 1 , ∞ )

5th Edition

ISBN: 9780321969576

Author: Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger

Publisher: PEARSON

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Question

Chapter 4.5, Problem 60E

To determine

To plot:

The graph of the function f(x)=x3−4xx2−x and label all the asymptotes. Also, find the domain x and y intercept of the graph.

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Chapter 4.5, Problem 59E

Chapter 4.5, Problem 61E

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Chapter 4 Solutions

College Algebra (5th Edition)

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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To plot: The graph of the function f ( x ) = x 3 − 4 x x 2 − x and label all the asymptotes. Also, find the domain x and y intercept of the graph.

To plot: The graph of the function f(x)=x3−4xx2−x and label all the asymptotes. Also, find the domain x and y intercept of the graph.

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Chapter 4 Solutions

To plot:

The graph of the function f(x)=x3−4xx2−x and label all the asymptotes. Also, find the domain x and y intercept of the graph.