Extra Credit Problems
First Quarter

Instructions:
  1.  Problems may be submitted any time during the quarter, but they MUST be turned in by the due date.
        (Due Date:  October 1, 2010)
  2.  Your work must accompany each problem.  No credit will be given for just an answer.
  3.  Parts of problems are worth anywhere from 1 - 3 points depending on level of difficulty.
       Credit is given only for correct work and answers. The whole part must be correct to
       receive credit.
  4.  You may do as many or as few problems as you desire. Try to keep them in order.

Problems 

1.  Solve:   

2.  Solve for x: 
 

3.  PQRS is a rectangle with vertices P(-4,-1) and Q(-6,5) and PQ = 2(QR).  Find the
     coordinates of R and S.
    (Problem taken from Advanced Mathematics by Richard Brown)

4.  Given  and , find the domain of f(g(x)).

5.  Sketch the graph of without the aid of a calculator.  Explain your
     reasoning.
     (Problem taken from Advanced Mathematics by Richard Brown)

6.  If f is a linear function such that f(x + 2) - f(x) = 6, find the value of f -1(x + 2) - f -1(x).
     (Problem taken from Advanced Mathematics by Richard Brown)

7.  Consider a commuter bus company that charges $2.00 per ride and receives about 1200 fares
     daily. It is estimated that for every $0.20 the fare is lowered, an additional 200 riders will take
     the bus. Find the fare that will maximize the bus company's revenue.

8.  A cylinder is generated by rotating a rectangle with perimeter 12 inches about one of its sides.
     a. Express the volume of the cylinder as a function of x.
     b. Give the domain of this function.
     c. Find the approximate value of x that maximizes the volume.
     d. Give the approximate maximum volume.

9.  Find a polynomial whose roots are double those of   y = x3 - 7x2 - 5x + 2.

10.  What happens to the roots of a polynomial when the coefficients are reversed?

11.  A cone with a height of 10 cm and a radius of 5 cm will increase in volume by 20% when the
       radius is increased and the height remains the same.  Find the increase in the radius.

12.  Find the maximum volume of a cylinder inscribed in a sphere with radius 10.

13.      Find   function

14.  Graph 
        Find the domain, range, and zeros.

15.  Find the domain of f(g(x))  and the domain of g(f(x))  when