Explanation Procedure used: “ Graphing a rational function: (1) Obtain the vertical asymptote and the domain of the rational function. (2) Obtain the horizontal asymptote and the oblique asymptote of the rational function. (3) Obtain the y -intercept by the evaluation of f ( 0 ) . (4) Obtain the x -intercept by solving f ( x ) = 0 . (5) Resolve whether the graph intersects its horizontal asymptote y = b by solving f ( x ) = b or its oblique asymptote y = m x + b by solving f ( x ) = m x + b where b is the y value of horizontal asymptote. (6) Determine an x -value in each interval of the domain obtained by the vertical asymptotes and x -intercepts. (7) Draw the graph.” Calculation: Step 1: Set the denominator of the given rational function equal to 0. If a is the zero of the denominator, then the line x = a is a vertical asymptote. Now set the denominator of the given rational function equal to 0. x 2 − 4 = 0 x 2 = 4 x = − 2 , 2 At x = − 2 and x = 2 , the denominator of the given rational function is 0. The numerator of the given rational function is not equal to 0 at these values of x . The equations of the vertical asymptote are x = − 2 and x = 2 . Since the domain cannot include the values x = − 2 and x = 2 , the domain of the given rational function is ( − ∞ , − 2 ) ∪ ( − 2 , 2 ) ∪ ( 2 , ∞ ) . Step 2: If the numerator and denominator have the same degree a and the function is of the form A x a + ⋯ + A 0 B x a + ⋯ + B 0 , where B ≠ 0 . Then divide the numerator and denominator of the above expression by x a to obtain the horizontal asymptote y = A B . In the given rational function, the numerator and denominator have the same degree. Divide the numerator and denominator of the given rational function by x 2 to obtain the horizontal asymptote as: y = 9 1 = 9 The equation of the horizontal asymptote is y = 9

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ISBN: 8220100802669

Author: Rockswold

Publisher: PEARSON

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Chapter 4.2, Problem 43E

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To draw: The graph of the rational function f(x)=9x2−1x2−4.

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Chapter 4.2, Problem 42E

Chapter 4.2, Problem 44E

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Chapter 4 Solutions

EBK GRAPHICAL APPROACH TO COLLEGE ALGEB

Ch. 4.1 - Provide a short answer to each question. Do not...Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Provide a short answer to each question. Do not...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 draw: The graph of the rational function f ( x ) = 9 x 2 − 1 x 2 − 4 .

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To draw: The graph of the rational function f(x)=9x2−1x2−4.

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Chapter 4 Solutions