Question

consider the rational function3x^2+25x+8__________x^2+7x-8Find the horizontal asymptote(s) or explain why there is none

Answer 1

We have the following:

$\frac{3x^2+25x+8}{x^2+7x-8}$

factoring:

$\frac{(3x+1)(x+8)}{(x-1)(x+8)}=\frac{3x+1}{x-1}$

now, the horizontal asymptote is:

if denominator degree> numerator degree, the horizontal asymptote is the x-axis: y = 0

if the degree of the numerator = 1 + the degree of the denominator, the slanted asymptote of the form y = mx + b

if the degrees are equal, the asymptote is the quotient of the principal coefficients of the numbered and denoninator, therefore

$\frac{3x}{x}=3$

Therefore the horizontal asymptote is

$y=3$