Question

Describe where the function has a vertical asymptote and EXPLAIN how you found your answer.


`f(x) (x^2 +7x+10)/(x^2+9x+20)`

Answer 1

x = -4

Explanation:

Vertical asymptotes are found where the denominator has a zero that is not cancelled by a numerator zero. Here, the expression simplifies to ...

`f(x)=(x^2+7x+10)/(x^2+9x+20)=((x+5)(x+2))/((x+5)(x+4))=(x+2)/(x+4) \qquad x\\e -5`

The function is undefined at x=-5, but has a vertical asymptote at x=-4.