Rational Functions: The Whole Thing 8

Horizontal asymptote:

Look at

x^3 / x^2 = x something

Hey -- it's a slant!

Slant 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 ) )

1 2 3 4 5 6 7 8 9 10

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