How can I create a rational function g(x) with these

Kiana Harper

Kiana Harper

Answered question

2022-05-22

How can I create a rational function g(x) with these requirements:
1. The vertical asymptotes are at 2 and 5
2. The function has a slant asymptote y=2x+1
3. The y-intercept is 7

Answer & Explanation

iberistazi

iberistazi

Beginner2022-05-23Added 10 answers

In order to fulfill the condition on the asymptotes we can set
f ( x ) = A ( x 2 ) ( x 5 ) + 2 x + 1
and by the condition f(0)=7 find out A, that is A=60, thus
f ( x ) = 60 ( x 2 ) ( x 5 ) + 2 x + 1

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