Question

What are the vertical asymptotes and holes for the graph of y=x+2/x^2+8x+15?

Answer 1

`"vertical asymptotes at "x=-5" and "x=-3`
`"there are no holes"`

Explanation:

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non-zero for these values then they are vertical asymptotes.

`"solve "x^2+8x+15=0rArr(x+3)(x+5)=0`

`rArrx=-5" and "x=-3" are the asymptotes"`

`"Holes occur when a common factor is eliminated from"`
`"the numerator/denominator. This is not the case here"`
`"hence there are no holes"`
graph{(x+2)/(x^2+8x+15) [-10, 10, -5, 5]}