Question

How do you find the asymptotes for `h(x) = (2x - 1)/ (6 - x)`?

Answer 1

vertical asymptote: `x = 6`
horizontal asymptote: `y = -2`

Explanation:

To find the vertical asymptote, set the denominator of the function equal to zero and solve for x:

`6-x = 0`
`-x = -6`
`x = 6`

To find the horizontal asymptote(s), find the following limits:

`y = \lim_{x\to infty}(frac{frac{2(x)}{(x)}-frac{1}{(x)}}{frac{6}{(x)}-frac{(x)}{(x)}}) = (frac{2-0}{0-1}) = frac{2}{-1} = -2`

`y = \lim_{x\to -infty}(frac{frac{2(-x)}{(-x)}-frac{1}{(-x)}}{frac{6}{(-x)}-frac{(-x)}{(-x)}}) = (frac{2+0}{0-1}) = frac{2}{-1} = -2`