Question

Consider the function f(x) = ax+3 over x-b.

Find a and b given that y=f(x) has asymptotes with equations x = -1 and y = 2.

Answer 1

f ( x ) = ( a x + 3 ) / ( x - b )
Vertical asymptote: at x = - 1 the equation goes to infinity.
x - b = 0
- 1 - b = 0
- b = 1
b = - 1
Horizontal asymptote: at y = 2

`\lim_(x \to \infty) (ax+3)/(x-b)=2`
It means that a = 2.