Question

Determine the equation of the vertical asymptote and the equation of the slant asymptote of the...

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    

Math   Precalculus   
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Homework Answers

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
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