Question

What are the values of a and b if the function has a horizontal asymptote at y = –2 and a vertical asymptote at x = 4?
f(x) 5/x+a +b

a = 4, b = 2

a = 4, b = –2

a = –4, b = 2

a = –4, b = –2

none of the answer choices

Answer 1

Assuming f(x) = 5/(x + a) + b:

- Vertical asymptote where denominator 0: x + a = 0 ⇒ x = −a. For x = 4 we need −a = 4 ⇒ a = −4.
- Horizontal asymptote is y = b (since 5/(x + a) → 0 as x → ±∞). For y = −2 we need b = −2.

So a = −4, b = −2.