Question

How do you find the vertical, horizontal or slant asymptotes for `f(x) = (x+4)/(x-2)`?

Answer 1

`x=2`
`y=1`

Explanation:

The equation is undefined when the denominator becomes 0. Consequently the excluded value is `x=2` thus there is a vertical asymptote at `x=2`

As the value of `x` increases significantly in both the positive and negative domains the influence of the constants of 4 and -2 becomes less and less significant.

Thus `lim_(x to+-oo) (x+4)/(x-2)-> x/x = 1`

So `y=1` is an asymptote.