4Horizontal asymptote:
 
Look atx^3 / x^2  =  x something

Hey -- it's a slant!

5Slant asymptote:

 

( x^3 + 0x^2 + 0x ) / ( x^2 - 9 ) gives ( x^3 - 9x ) ... subtracting gives 9x  ...  stop here since x^2 no longer goes in


The line y = x


OK, Skippy -- are you ready to graph this bad boy?

Intercepts and asymptotes:


the intercepts and asymptotes for f( x ) = ( 3x ) / ( ( x - 2 )( x + 4 ) )