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Rational Functions - The Whole Thing

What about the middle neighborhood?

We'll need to quickie plot two points...  Try it before going on.

f( x ) = ( x^3 ) / ( ( x - 3 )( x + 3 ) ) plugging in -1 for y gives ( - ) / ( ( - )( + ) ) = ( + ) ... above for y , plugging in 1 for y gives ( + ) / ( ( - )( + ) ) = ( - ) ... below for y


graph of f( x ) = ( x^3 ) / ( ( x - 3 )( x + 3 ) )

NOTE:  A common mistake that students make is to think that a graph cannot cross a slant or horizontal asymptote.  This is not the case!  A graph CAN cross slant and horizontal asymptotes (sometimes more than once).  It's those vertical asymptote critters that a graph cannot cross.  This is because these are the bad spots in the domain.

YOUR TURN:

Graph

f( x ) = ( 4 - 3x - x^2 ) / ( x - 2 )