Explanation Definition used: “For a rational function f ( x ) = p ( x ) q ( x ) , where p ( x ) and q ( x ) are polinomials with no common factors other than constants, if a is a zero of the denominator, then the line x = a is a vertical asymptote for the graph of the function.” “When the numerator and the denominator of a rational function have the same degree, the line y = a / b is the horizontal asymptote, where a and b are the leading coefficients of the numerator and the denominator, respectively. When the degree of the numerator of a rational function is less than the degree of the denominator, the x -axis, or y = 0 , is the horizontal asymptote. When the degree of the numerator of a rational function is greater than the degree of the denominator, there is no horizontal asymptote.” “When the degree of the numerator is 1 greater than the degree of the denominator, there is an oblique asymptote.” Calculation: Given function is g ( x ) = x 2 + 4 x − 1 x + 3 . Here, the rational function is g ( x ) = x 2 + 4 x − 1 x + 3 , where p ( x ) = x 2 + 4 x − 1 and q ( x ) = x + 3 are polynomials with no common factors. In order to obtain the vertical asymptote for the graph of the function, find the zero of the denominator as follows: x + 3 = 0 x = − 3 Thus, by above result, the vertical asymptote is the line x = − 3 . Since the degree of the numerator is greater than the degree of the denominator, the rational function has no horizontal asymptote. Here, it is observed that the degree of the numerator is 1 greater than the degree of the denominator. From the above definition, it is to be cleared that the function g ( x ) = x 2 + 4 x − 1 x + 3 has an oblique asymptote exist

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ISBN: 9780135834398

Author: BITTINGER

Publisher: PEARSON

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Chapter 4.5, Problem 27E

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The oblique asymptote of the function g(x)=x2+4x−1x+3.

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MYMATHLAB W/PEARSON ETEXT---18 WEEK STA

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

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The oblique asymptote of the function g ( x ) = x 2 + 4 x − 1 x + 3 .

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The oblique asymptote of the function g(x)=x2+4x−1x+3.

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