exercise 10 Which of the following indicates that the graph of the function f(x)has a horizontalasymptote at y = 0?O (**) limo+ f(x) = +∞olimx→+∞ f(x) = 0(*) limo- f(x) = =18both (*) and (**)

Given the function f(x). The objective is to find for which of the options indicates that the graph…

Answered: Which of the following indicates that…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 8E

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sketch the graph of y = x^3 / (x^2 - 4), keep in mind the information provided:1. x and y intercept: (0, 0)2. Vertical asymptotes: x = 2, x = -23. There is no horizontal asymptote.4. Discontinuity at x = -2 and x = 2.5. First derivative: y’ = (x^4 - 12x^2) / (x^2 - 4)^26. Critical points: x = 0, x = 2√3, x = -2√37. Intervals of increase: (-∞, -2√3) U (2√3, ∞)8. Intervals of decrease: (-2√3, -2) U (-2, 0)9. Local maxima: (-3.46, -5.20) and (3.46, 5.20)10. Second derivative: y’’ = (8x^3 + 96x) / (x^2 - 4)^311. Critical numbers: (0, 0), (√12, 3√3), (-√12, -3√3)12. Point of inflection: (0, 0)13. Concave upward: (-2, 0) U (2, ∞)14. Concave downward: (-∞, -2) U (0, 2) A sketch of the graph (by hand) - Labeling of vertical asymptotes on the sketch - Labeling of horizontal asymptotes on the sketch - Labeling of x and y intercepts on the sketch - Labeling of maximum and minimum points on the sketch - Labeling of points of inflection on the sketch A sketch of the graph on Desmos with all key…

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Which of the following indicates that the graph of the function f(x)has a horizontal asymptote at y = 0? (**) limo+ f(x) = +∞o limx→+∞ f(x) = 0 (*) limo- f(x) = =18 both (*) and (**)

Which of the following indicates that the graph of the function f(x)has a horizontal asymptote at y = 0? (**) limo+ f(x) = +∞o limx→+∞ f(x) = 0 () limo- f(x) = =18 both () and (**)