Question

State the horizontal asymptote of the rational function.

f(x) = x+9/x^2+8x+5

Answer 1

0.
In Calculus, we are taught shortcuts to answer these HA questions. :)
1. The numerator and the denominator have the same degree (meaning, same exponents for the FIRST coefficient-variable pairing) the HA is their coefficients.
2. The degree of the numerator is less than the degree of the denominator (the exponent of the numerator is smaller than the exponent of the denominator) the HA is 0. This is like your example.

Answer 2

Examples:
\[\frac{x}{5x}\] = HA is 1/5.
\[\frac{ 3x^2 }{ 5x^4 }\] = HA is 0.

Answer 3

Oh, that helps, Thanks:)

Answer 4

No problem!