Question

How do you find the vertical, horizontal or slant asymptotes for `f(x)=(1-5x)/( 1+2x`?

Answer 1

`y = -(5)/(2)`

`x = -1/2`

Explanation:

Firstly, find what `x` cannot be for the vertical asymptotes

So the denominator of the fraction cannot be equal to `0`.

`1+2x != 0`
`x!= -0.5`

Meaning that `x = -0.5` is the vertical asymptote.

Then, find the horizontal/slant asymptotes by only looking at the highest degree of `x`.

`f(x) = (1-5x)/(1+2x)`

As `x rarr oo`, we only care about the values that will change the function most, so we can just look at the highest degree of `x`. Thus, he asymptote will be:

`y = (-5x)/(2x)`

`y = -(5)/(2)`