Asked by Norma
Whats a function that has a hole at (6, 11), no horizontal asymptote and resembles the line y = 3x - 7.
Answers
Answered by
oobleck
You don't say anything about a vertical asymptote, so let's assume there is none. To get the asymptote of y=3x+7, we could use
y = 3x+7 + (ax+b)/(x^2+1)
To have y(6) = 11 we can use
y = 3x+7 - (70x+98)/(x^2+1) = (3x^3+7x^2-67x-91)/(x^2+1)
Now, to get the hole at x=6, just add a factor of (x-6) top and bottom
y = (3x^3+7x^2-67x-91)(x-6) / (x^2+1)(x-6)
= (3x^4 - 11x^3 - 109x^2 - 311x + 546) / (x^3 - 6x^2 + x - 6)
y = 3x+7 + (ax+b)/(x^2+1)
To have y(6) = 11 we can use
y = 3x+7 - (70x+98)/(x^2+1) = (3x^3+7x^2-67x-91)/(x^2+1)
Now, to get the hole at x=6, just add a factor of (x-6) top and bottom
y = (3x^3+7x^2-67x-91)(x-6) / (x^2+1)(x-6)
= (3x^4 - 11x^3 - 109x^2 - 311x + 546) / (x^3 - 6x^2 + x - 6)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.