Question

Write a rational function that has the vertical asymptote x = 1 and the horizontal asymptote y = 2.

Answer 1

f(x) = 2x / (x - 1)

Explanation:

One such function would be:

2x

f(x) = -----------

x - 1

f(x) is undefined at x = 1, so has a vertical asymptote at x = 1.

As x increases without bound, f(x) approaches (2x) / (x), or just 2. Thus, f(x) has the horiz. asy. y = 2.