graphing and solving variables?

Question

http://img58.imageshack.us/img58/8492/img0638zc7.jpg

for q.14, what is c) and e) referring to?

for q.15, is a = -2 and b = -6 correct?

so is there a horizontal asymptote at -1?

CONCLUSION?
http://img385.imageshack.us/img385/7910/img0638fq6.jpg

Answer 1

Part (c) means the graph approaches -1 as x gets large and the graph diverges in a negative directions as x gets smaller. Part (c) refers to end-behavior of the function.

Part (e) means there is a vertical asymptote at x = 3.

In question 15, a = -2 and b = -6 is not correct. a = 4, b = -12 are the correct answers. How did I find these?

I solved the following system of equations:

-a - b = 8
3a + b = 0

I obtained the first equation by plugging in -1 for x in f.
I obtained the second equation by differentiating, plugging in -1 for x, then setting the simplified derivative equal to 0.

EDIT: Yes, there is a horizontal asymptote at y = -1, but it's not a bell curve as you have drawn. The graph only approaches -1 as x goes to positive infinity. Also, don't forget the vertical asymptote at x = 3.

Answer 2

For C) it is basically just telling you that if you go way out to the right then the function just becomes y=-1; similarly, if you go way out to the left, the function gets smaller and smaller.
For E, it just says that as you approach the point from different directions, the limit is the same.