Question

Which function has a graph with a horizontal asymptote at y = 3, a vertical asymptote at x = 1, and an x-intercept at 2?
f(x)=x -1 / 3(x-2)

Answer 1

One convenient choice is
f(x) = 3 − 3/(x − 1),
which can be written f(x) = 3(x − 2)/(x − 1).

Check:
- Vertical asymptote: denominator 0 at x = 1.
- Horizontal asymptote: as x → ±∞, f(x) → 3 (leading-coefficient ratio 3/1).
- x-intercept: f(2) = 3(0)/(1) = 0.

(If you meant f(x) = (x−1)/(3(x−2)), that would have a vertical asymptote at x = 2 and horizontal asymptote y = 1/3, so it doesn't meet the given conditions.)