4, 5] state the horizontal asymptote of the rational function. f(x) = quantity x plus nine divided by quantity x squared plus two x plus three.

the denominator polynomial has a higher degree than the numerator polynomial, so it will get large faster for large values of x. the result will tend to zero. hence the appropriate choice is

y = 0

the numerator changes sign at x=-9, but the denominator is always positive. hence the quotient will be negative for x < -9 and will be positive for x > -9. that is, the asymptote will be approached from below on the left, but from above on the right.

1/5^2 = 7.56/45