Write an equation for a rational function with: Vertical asymptotes at x = 5 and...

porfiru1nm

porfiru1nm

Answered

2022-12-31

Write an equation for a rational function with: Vertical asymptotes at x = 5 and x = -4 x intercepts at x = -6 and x = 4 Horizontal asymptote at y = 9?

Answer & Explanation

funjisnickenskdg

funjisnickenskdg

Expert

2023-01-01Added 3 answers

(1) Given that there are vertical asymptotes at x=5 and x=-4, the factors in the denominator are (x-5) and (x+4).
(2) As we have x-intercepts at x=-6 and x=4, we have (x+6) and (x-4) in numerator as factors
(3) As we have horizontal asymptote at y=9, the highest power of numerator and denominator are same and coefficient of numerator is 9 times that of denominator
Hence, rational function is 9(x+6)(x4)(x5)(x+4) or 9x2+18x216x2x20

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