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Rational Functions - The Whole Thing

 

YOUR TURN:

Graph

f( x ) = ( x - 3 ) / ( x^2 - 3x - 10 )

(You've already done all the pieces!)

* Remember that, when you are working these things out -- write out all of your work in a neat and organized way!  This is one of the main reasons you have to take math classes -- they teach you to organize your thoughts AND TO THINK!

One last problem:

Graphf( x ) = ( x^3 ) / ( x^2 - 9 )

2 things
and
2 sentences!

 
1The y-intercepts:  Find f(0)
 
f( 0 ) = ( ( 0 )^3 ) / ( ( 0 )^2 - 9 ) = 0( 0 , 0 ) nowhere else!

 

2The x-intercepts:  numerator = 0, solve

 

x^3 = 0

( 0 , 0 ) nowhere else!

 
3Vertical asymptotes:  denominator = 0, solve
 
x^2 - 9 = 0 ... ( x - 3 )( x + 3 ) = 0 ... x = 3 , x = -3The lines x = -3 and x = 3