find horizontal asymptotes

Question

find horizontal asymptotes

              2

f(x)= 5x     -6x- 6

___________________=

             2

        4x     -7+4

 

 

          2

F(x)=x +5x-1

_______________=

        x-1

 

 

 

 

 

 

 

 

Answer 1

For f(x) = (5x²-6x-6)/(4x²-7+4), the degree of the numerator = the degree of the denominator, so the horizontal asymptote occurs at the ratio of the highest degree terms:

 

y = 5x²/4x²

 

y = 5/4

 

For f(x) = (x2+5x-1)/(x-1), the degree of the denominator is one less than the degree of the numerator, so we will have a slant asymptote.  To find the equation of the asymptote's line, divide the numerator by the denominator and drop any remainder.

 

        x + 4    

x-1 ) x2+5x-1

      -(x2 +x)

       --------

             4x-1

          -(4x-1)

           -------

                  0 (no remainder)

 

The slant asymptote is y = x + 4