### Home > CALC > Chapter 1 > Lesson 1.2.3 > Problem1-51

1-51.

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

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

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

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 $x → -∞$ ?

Refer to the hint in part (a).

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

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)?

Refer to the hint in part (c).