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Rational Functions - More on Limits

We'll need a notation to distinguish between the right and left:

Approaching x = 2 from the left:x approaches 2 from the left
 
Approaching x = 2 from the right:x approaches 2 from the right


So...

As x approaches 2 from the left , f( x ) goes toward -infinity

As x approaches 2 from the right , f( x ) goes toward infinity
 

What about as Pierre runs towards x = -2 ?


If he's coming in from the right, he's climbing up.

 

 

If he's climbing in from the left, he's climbing down.

Pierre the Moutain Climbing Ant is climbing down when he's coming in from the left ... he's climbing up when he's coming in from the right

Again, it matters whether he's coming in from the right or the left:

As x approaches -2 from the left , f( x ) goes toward -infinity

As x approaches -2 from the right , f( x ) goes toward infinity