Please answer (a). thank you r* – 4x2r(x + 8)(x – 2)8(7x – 4)Given: f(x) =with f'(x) =and f"(x) =(x+ 2)?(r+ 2)³3(r+ 2)4(a) Find the domain of f and the intercepts of the graph of f.(b) Using limits, show that r = -2 and y = x – 8 are linear asymptotes of the graph of f.(c) Identify the critical numbers of f and the possible points of inflection of the graph of f.(d) Construct a table of signs for f' and f". Specify the following:i. the intervals on which f is increasing or decreasing, and on which the graph of ƒ is concaveup or concave down, andii. the values of r at which f has relative extrema, inflection points, and vertical asymptotes(if any).(e) Sketch the graph of f with emphasis on concavity. Label all the intercept points, relativeextremum points, and inflection points with their coordinates. Show the linear asymptotes ofthe graph of f and label them with their respective equations.

Note: Since, the student has mentioned to solve only part (a), so we are going to solve only part…

Answered: Given: f(x) = with f'(x) = r(x+8)(x –…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 54E

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Given: f(x) = with f'(x) = r(x+8)(x – 2) and f"(x) = 8(7x – 4) %3D (r+2)² ' (r+ 2)³ (r+ 2)ª (a) Find the domain of f and the intercepts of the graph of f.