Question
Question: Create a rational function f(x) such that the function has:
2 vertical asymptotes
1 hole
1 positive horizontal asymptote
2 vertical asymptotes
1 hole
1 positive horizontal asymptote
Answers
oobleck
2 vertical asymptotes
y = 1/(x^2-1)
a hole
y = (x+2) / (x+2)(x^2-1)
a horizontal asymptote. y > 0
needs top and bottom to be of the same degree
y = (x+2)^3 / (x+2)(x^2-1)
asymptote is y=1
y = 1/(x^2-1)
a hole
y = (x+2) / (x+2)(x^2-1)
a horizontal asymptote. y > 0
needs top and bottom to be of the same degree
y = (x+2)^3 / (x+2)(x^2-1)
asymptote is y=1