Analyze the graph of $y = \frac { ( x + 2 ) ( x - 1 ) } { x - 1 }$ at right.

1. What does $y$ approach as $x → ∞$ ?

   Hint (a):

   The graph appears to be the linear function $y = x + 2$, with a hole at $(1,3)$.

   Answer (a):

   Just like the graph of $y = x + 2$, this function will go up ($y →+∞$) as we move to the right ($x →∞$)

2. What does $y$ approach as $x → -∞$ ?

   Hint (b):

   Refer to the hint in part (a).

3. What does $y$ approach as $x → 1^-$ (from the left)?

   Hint (c):

   As the graph approaches the hole from the left ($x → -1$), what $y$-value does it approach?

4. What does $y$ approach as $x → 1^+$ (from the right)?

   Hint (d):

   Refer to the hint in part (c).