I don't have a single clue to solve the following question so I post here to seek help.?

2017-11-11 1:00 am
Create a polynomial function f(x) with a least two vertical asymptotes, and a non-zero horizontial asymptote.



Demonstrate how you would find the x-values in which f(x) ≥ 5




How is this different from finding where f(x) ≥ y ?







Thank you very much

回答 (1)

2017-11-13 1:57 pm
✔ 最佳答案
f(x)= 2 x^2 /[(x-1)(x-2)]
two vertical asymptotes : x =1 , x = 2
a non-zero horizontial asymptote : y = 2

f(x) ≥ 5 ---> 5(x-1)(x-2) ≥ 2 x ^2
5 x^2 - 15 x + 10 ≥ 2 x^2
3 x^2 - 15 x + 10 ≥ 0

f(x) ≥ y ---> y(x-1)(x-2) ≥ 2 x ^2
y(x^2-3x+2)≥ 2 x ^2
(y-2) x^2 - 3y x + 2y ≥ 0


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