Question

Determine the equation of the vertical asymptote and the equation of the slant asymptote of the rational function.
f(x)=−24x2−14x−5/3x+1

The equation of the vertical asymptote is    
The equation of the slant asymptote is    

Answer 1

Given function is :

This is a polynomial function .

Finding Vertical asympote:

Set denominator= 0

3x+1=0

3x=-1

x=-1/3

Vertical asymptote , x =

The equation of vertical asymptote is:

Given function is

Here degree of numerator = 2

Degree of denominator= 1

If degree of numerator = 1+ degree of denominator we will have oblique/ slant asymptote

here ,    2 =1+1

so we have oblique asymptote here

So get the equation of the slant asymptote , we have to do long division

Long division:

Slant asymptote is y=-8x-2

The equation of slant asymptote is:

y=-8x-2