Question

State the horizontal asymptote of the rational function. x+9/x^2+2x+5

Answer 1

For determining horizontal asymptotes of rational functions like this, follow these rules:
1. If the degree of the numerator is greater than the denominator, there is no horizontal asymptote.
2. If degrees are same, divide the ratios of the highest degree monomial.
3. If the denominator has a higher degree than the numerator, then the horizontal asymptote is at y = 0.

The 'degree' is the highest exponent on a variable.
For example, in the polynomial 3x^4 + 8x^2 - x - 8, the degree of this polynomial is 4, since '4' is the highest power.