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Rational Functions - The Whole Thing

OK...  what were the 2 things?
 

1intercepts
2asymptotes

What were the 2 sentences?

1These guys are functions.
2Graphs hug asymptotes.

Let's do some graphing, baby!

Graphf( x ) = ( 2x^2 + 5 ) / ( x^2 - 25 )

2 things
and
2 sentences!

 
1The y-intercept:  Find f(0)
 

f( 0 ) = ( 2( 0 )^2 + 5 ) / ( ( 0 )^2 - 25 ) = -1 / 5

( 0 , -1 / 5 ) ... nowhere else!
 

2The x-intercept:  Set numerator = 0 and solve

 

2x^2 + 5 = 0
Since we only deal with real numbers when graphing, this has no solution!

* Do you see why?

It will never cross the x-axis
This is going to be very useful info!