Explanation Given information: The function is g ( x ) = 8 x − 1 + 27 x + 4 . Calculation: Consider the function. g ( x ) = 8 x − 1 + 27 x + 4 The vertical asymptote is, lim x → 4 + g ( x ) = ∞ lim x → 4 − g ( x ) = − ∞ lim x → 1 + g ( x ) = ∞ lim x → 1 − g ( x ) = − ∞ Hence, the vertical asymptotes is x = − 4 , 1 . The horizontal asymptote is, lim x → ∞ g ( x ) = 0 Hence, the horizontal asymptotes is y = 0 . Differentiate the function. g ′ ( x ) = − 8 ( x − 1 ) 2 − 27 ( x + 4 ) 2 Hence, the function is decreasing for all x

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 4.4, Problem 39PS

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To explain: The point where the graph of given function is rising, falling, the concavity, the point of inflection and vertical and horizontal asymptotes.

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Chapter 4.4, Problem 38PS

Chapter 4.4, Problem 40PS

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The point where the graph of given function is rising, falling, the concavity, the point of inflection and vertical and horizontal asymptotes.

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