Question

For what values of x, if any, does `f(x) = 1/((5x+8)(x+4)` have vertical asymptotes?

Answer 1

`x` = `-4` and `-8/5`

Explanation:

So, a vertical asymptote is a line that extends vertically to infinity. If we notice, it implies that the y co-ordinate of the curve much reach Infinity.

We know that infinity = `1/0`

So, when compared with `f(x)`, it implies that the denominator of `f(x)` should be zero. Hence,

`(5x+8)(x+4)` = `0`

This is a quadratic equation whose roots are `-4` and `-8/5`.

Hence, at `x` = `-4`, `-8/5` we have vertical asymptotes