Explanation Calculation: Consider the function, h x = x 3 − 4 x 2 x 2 + 3 x + 2 . According to the method of finding the vertical and horizontal asymptotes as shown below, Consider f x to be the rational polynomial function, f x = N x D x = a n x n + a n − 1 x n − 1 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + a 1 x + a 0 b m x n + b m − 1 x m − 1 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + b 1 x + b 0 Where N x and D x are polynomials and D x is not a zero polynomial. Then, the graph of f has vertical asymptotes at the zeros of D x . The graph of f has at most one horizontal asymptote can be determined by comparing the degrees of N x and D x . If n < m , then the graph of f has line y = 0 (the x-axis) as a horizontal asymptote. If n = m , then the graph of f has line y = a n b m (ratio of the leading coefficients) as a horizontal asymptote

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ISBN: 9781337282291

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 4, Problem 10RE

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To calculate: All vertical and horizontal asymptotes of the graph of the function, hx=x3−4x2x2+3x+2.

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Chapter 4, Problem 9RE

Chapter 4, Problem 11RE

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All vertical and horizontal asymptotes of the graph of the function, h x = x 3 − 4 x 2 x 2 + 3 x + 2 .

Solution Summary: The author explains the method of finding the vertical and horizontal asymptotes of the function.

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To calculate: All vertical and horizontal asymptotes of the graph of the function, hx=x3−4x2x2+3x+2.

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Chapter 4 Solutions