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How about this one?

f ( x ) = ( 3x ) / ( x^2 + 2x - 8 )

graph of f ( x ) = ( 3x ) / ( x^2 + 2x - 8 ) ... Pierre is sliding downhill in every section

It's one wild ride for Pierre!  Downhill sledding all the way!  But, if we said that f is decreasing everywhere, that wouldn't be quite right...  Because the graph doesn't exist at x = -4 and x = 2.

It's decreasing everywhere on its domain, which is

( -infinity, -4 ) U ( -4 , 2 ) U ( 2 , infinity )


YOUR TURN:

Given

  f ( x ) = ( x^2 - x - 6 ) / ( x^2 - 1 )

Find the intervals where f is decreasing.

Find the intervals where f is increasing.


Given

  f ( x ) = ( x^2 ) / ( x^2 - 4 )

Find the intervals where f is decreasing.

Find the intervals where f is increasing.