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:

`(3x^2+25x+8)/(x^2+7x-8)`

factoring:

`((3x+1)(x+8))/((x-1)(x+8))=(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

`(3x)/(x)=3`

Therefore the horizontal asymptote is

`y=3`