(1) (10 points)

(a)  

(b) Find all the x values that are not in the domain of the function .

(2) (10 points)

(a) Sketch the graph of the equation    .

(b) Find the equation of the line that is parallel to the graph of    (from Part a, above) and which passes through the point . Put your final answer in slope-intercept form, and simplify as much as possible.

(3) (10 points)  Consider the functions and   

(a)

(b)



(4)  (20 points)  Evaluate the following limits.

(a)    

(b)  

(c)    

(d)    

(5) (35 points) This problem concerns the function  .

(a) State the domain of f.

(b)    

(c)    

(d)    

(e)    

(f) List the vertical asymptote(s) of f  (if any).  (Feel free to use any relevant information from parts a-d above)

(g) List the horizontal asymptote(s) of f  (if any).   (Feel free to use any relevant information from parts a-d above)

(6) (10 points)  This problem concerns the function
(a)

(b)

(c)

(d)

(e) Is f continuous at x = 0? (Explain, using above information.)

(f)

(g)

(h)

(i)

(j) Is f continuous at x = 1? (Explain, using above information.)



(7) (5 points) Sketch the graph of a function f  satisfying the following properties:  ,   ,   ,  ,   and   ,  There are many correct answers.