Sketch the graph of the two functions below. Compare the equations and their graphs. Then write a complete set of approach statements for each.

1. $y = \frac { ( x + 6 ) ( x - 1 ) } { x - 1 }$

   Hint (a) and (b):

   For parts (a) and (b).
   One of the functions has a hole and the other has an asymptote.

   More help (a):

   Refer to Lesson 1.2.3, problems 1-44 & 1-45.
   A complete set of approach statements include:
   $x → −∞$
   $x →$ (hole)^{$^{−}$}
   $x →$ (vertical asymptote)⁻
   $x → ∞$
   $x →$ (hole)^{$^{+}$}
   $x →$ (vertical asymptote)^{$^{+}$}

2. $y = \frac { ( x + 6 ) ( x - 1 ) } { x - 2 }$

3. Explain why one graph has a hole while the other has a vertical asymptote.

   Hint (c):

   How does algebra help determine the location of holes and vertical asymptotes?

4. Find the end behavior of each graph.

   Hint (d):

   Horizontal asymptotes, if they exist, are the same as end behavior. If there is no horizontal asymptote, find end behavior with polynomial division (ignore the remainder).