See attached study guide.

1. Solve the inequality x^{2 Â} Â³ 6x and write the solution set in interval notation.             

                                                                                                     (no explanation required)                         1. ______ 

A.        [6, ¥)

B.        (–¥, 0]  È [6, ¥)

C.        (–¥, 6]  È [0, ¥)

            D.        [0, 6]

 

 

2.  Solve   £ 0 and write the solution set in interval notation.                   2. ______ 

                                                                                                      (no explanation required)                            

A.        (1, 7)

B.        (–¥, –4]

C.        (–¥, –4] È (1, 7)

            D.        [–4, 1) È (7, ¥)                                          

 

 

3.  For f (x) =  x⁴ + x – 3, use the Intermediate Value Theorem to determine which interval must contain a zero of f.              (no explanation required)                                  3. _______

A.        Between -3 and -2

B.        Between -2 and -1

C.        Between -1 and 0

D.        Between 0 and 1

 

 

4. Translate this sentence about area into a mathematical equation.

The distance an object falls, D, is directly proportional to the square of the time of the fall, t.

 

 

 

 

5.  Look at the graph of the quadratic function and complete the table.      [No explanations required.]

Graph	Fill in the blanks	Equation
Â	  State the vertex:   ____________   State the range:   _____________   State the interval on which the function is decreasing:   _____________	  The graph represents which of the following equations?      Choice:____     A.    y  =   –2x2 + 2x – 1   B.    y  =  –x2 – 2x + 3   C.    y  =  2x2 + 4x +3   D.    y  =   x2 + 2x – 1   Â

 

6.  Each graph below represents a polynomial function. Complete the following table.

(no explanation required)

              Graph	                            Graph A	                          Graph B
Is the degree of the polynomial odd or even? (choose one)	Â	Â
Is the leading coefficient of the polynomial positive or negative? (choose one)	Â	Â
How many real number zeros are there?	Â	Â

 

7. Let  When factored,  

(a) State the domain.

 

 

 

(b) Which sketch illustrates the end behavior of the polynomial function?

A.     Â

B.Â

C.

D.

 

 

Answer:  ________

 

 

(c) State the y-intercept:

 

 

 

(d) State the real zeros:

 

 

 

(e) State which graph below is the graph of P(x).  ___________

 

GRAPH A.  (below)                                                                           GRAPH  B.  (below)

 

 

 

 

 

 

 

 

 

 

 

 

                                                                                   

GRAPH  C.  (below)                                                                          GRAPH  D.  (below)

                                                                                

 

 

 

 

 

 

 

 

 

 

 

 

8. Let .    (no explanations required)

 

      (a)  State the y-intercept.

 

 

      (b) State the x-intercept(s).

 

 

      (c) State the vertical asymptote(s).

 

 

      (d) State the horizontal asymptote.

 

 

 

9. Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.

                                                                                                                                                        

     

 

10. Which of  the following functions is represented by the graph shown below? Explain your answer choice. Be sure to take the asymptotes into account in your explanation.

 

                                                                                                                                                        10. _____

A. 

 

B. 

                                                                                

C. 

 

D. 

 

11. For z = 3 - 2i and w = 4 +i, find z/w. That is, determine       and simplify as much as possible, writing the result in the form a + bi, where a and b are real numbers. Show work.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12. Consider the equation  x² + 29 = 4x. Find the complex solutions (real and non-real) of the equation, and simplify as much as possible. Show work.

 

 

 

13.   

The cost, in dollars, for a company to produce x widgets is given by C(x) = 5250 + 7.00x for

x ³ 0, and the price-demand function, in dollars per widget, is p(x) = 45 - 0.02x for 0 £ x £ 2250.

 

In Quiz 2, problem #10, we saw that the profit function for this scenario is

              P(x) = - 0.02x² + 38.00x - 5250.

 

(a) The profit function is a quadratic function and so its graph is a parabola.

 

      Does the parabola open up or down? __________

 

(b) Find the vertex of the profit function P(x) using algebra. Show algebraic work.

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) State the maximum profit and the number of widgets which yield that maximum profit:

 

 The maximum profit is _______________    when ____________  widgets are produced and sold.

 

(d) Determine the price to charge per widget in order to maximize profit.

 

 

 

 

(e) Find and interpret the break-even points. Show algebraic work.