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Final Exam Review Part 1

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Final Exam Review Part 1 Powered By Docstoc
					MATH 110

  Review
                Jeopardy
Functions   Straight as     Word     Pieces
             an arrow     Problems
  100           100          100      100

  200          200          200       200

  300          300          300       300

  400          400          400       400

  500          500          500       500
             Final Jeopardy?
•   Final Exam:
•   Monday May 9th, 2005
•   8:00am to 10:00am
•   Room PAS 201
•   Get to the exam no later than 7:45am
              Functions 100
• Which of the tables express y as a function of x?
        x      -2       0     -1     0      4
        y      5        1      3     1      5

        x      2        -2    0      2      4
        y      5        4     3      2      1

        x      1        2     1      4      5
        y      0        3     -2     1      9

        x      1        2     -3     4      6
        y      3        1      3     -1     5



• Answer: 1st and 4th
            Functions 200
• Find the domain of the function given
  below:



             f x  
                       2x
                      3 x
• Answer: [0,3)
                                      Functions 300
• The graphs of f(x) and g(x) are shown.
                          
                              y                                                              y

                                                                                         

                                                                                        

                                                                                         
                          
                                                                                         

                                                                                         
                          
                                                                                         
                                                  x                                                                      x

                                                                                          
                                                                                        
                         
                                                                                        

                                                                                        
                         
                                                                                        

                                                                                      

                                                                                        
                         
                                                                                        



                    f(x)                                                           g(x)

• Find the domain and range of each function
• Answer: f(x) D: [-3,infinity) R: [-4,infinity)
            g(x) D: [-5,5] R: [-3,3]
             Functions 400
• Which of the functions shown has a domain of
  all real numbers except 18?


                 f  x   x  18

                 g x  
                            2x
                          x  18
                 hx   2
                              1
                          x  324
• Answer: g(x)
               Functions 500
• A 24 inch wire is cut into 4 pieces to form
  a rectangle whose shortest side has a
  length of x. Express the area of this
  rectangle as a function of x. What is the
  domain of this function?



• Answer: Ax   x 12  x ; D : (0,12 )
     Straight as an Arrow 100
• Suppose that the quantity sold, q, of a
  particular product can be expressed as a
  linear function of the product’s price, p, by
  the linear function q(p) = -50p + 2000.
  Determine the slope of the graph of q(p)
  and interpret the slope in practical terms.
• Answer: slope is -50; this means that the
  amount sold decreases by 50 when the
  product’s price increase by $1.00.
     Straight as an arrow 200
• Find the coordinates of the x and y
  intercepts of 3x + 7y -1 =0.

• Answer: x-int (1/3,0) ; y-int (0, 1/7)
     Straight as an arrow 300
• A small electrical co-op in rural Arizona
  charges its customers a $5.00 basic
  monthly fee plus $0.12 per kilowatt hour
  used. Write a function to represent the
  monthly charge in dollars on an electric bill
  in terms of the number of kilowatt hours
  used.
• Answer: f(x) = 0.12x+5.00
     Straight as an arrow 400
• Determine whether the following table is a
  linear function. If it is find the equation of
  the line.
         x     1      2      3      4     5
         y     3     5.1    7.2    9.3   11.4




• Answer: yes constant rate of change;
  equation y = 2.1x +0.9
     Straight as an arrow 500
• Find the equation of the line perpendicular
  to 2x – y = 3 which passes through the
  point (1,3).



• Answer: y = -0.5(x-1)+3
        Word Problems 100
• A couple invests $3500 to build a rose
  garden. On average, it costs them $0.35
  to grow each rose. If each rose can be
  sold for $1.75, how many roses must be
  sold to break even?

• Answer: 2500 roses
        Word Problems 200
• A shop owner wants to mix high quality
  coffee beans that cost $5.00 per pound
  with cheap, crummy tasting beans that
  cost $1.00 per pound to get 20 pounds of
  a blend which should be worth $3.50 per
  pound. How much of the cheap blend
  should be used?

• Answer: 7.5 pounds
        Word Problems 300
• You invest $1000 in two accounts. The
  first pays 6% annual interest, the other
  pays 9% annual interest. At the end of
  one year you collect $84.60 in interest.
  How much was invested in each account?

• Answer: $180 in the 6% account and
  $820 in the 9% account.
         Word Problems 400
• A train that is traveling 52 mph leaves the
  station and goes west. Another train
  leaves the station on a parallel track 1
  hour later traveling west at 65 mph. How
  long until the fast train catches up with the
  slow train?

• Answer: 5 hours
           Word Problems 500
• A rancher wishes to enclose two adjacent rectangular
  corrals such that the right-hand corral has twice the
  length of the left hand (see diagram). She has 900 feet
  of fencing. Express the area of the enclosure as function
  of the length.      Answer: Al   3l 300  2l 
               Pieces 100
Which of the following represents the piece-
 wise function shown below?
Answer: c
                      Pieces 200
• Sketch the graph of the piece-wise defined
  function shown below:
                          x  1 if                    x 1
                f x   
                           2 x if                    x 1
                                               y

                                           

                                           

                                           

                                           

                                           

                                           
                                                                           x

                                                         
                                          

                                          

                                          

                                          

                                          

                                          

                                          
                Pieces 300
• Find g(0) for the function given below:

                      2 x 2  4 x if   x 1
             g x   
                       x2        if   x 1



• Answer: -2
                 Pieces 400
• Write the piece-wise function for the graph
  shown:




• Answer:             2.5 x  5.5
                      4
                                     if    3  x  1
            f x    x  2   1 if   1  x  2
                      3
                      2x  5        if    2 x3
                          Pieces 500
• The following table gives the Tax Rate Schedule for a person whose
  filing status was single during the year 2003.
             Adjusted
             gross                                 of the
             income is    but not                  amount
             over         over     Tax Due         over . . .
                   $0       7,000       10%             $0
                 $7,000     28,400  $700.00+15%      $7,000
                $28,400     68,800  $3910.00+25%    $28,400
                $68,800    143,500 $14010.00+28%    $68,800
               $143,500    311,950 $34926.00+33%   $143,500
               $311,950            $90514.50+35%   $311,950


• Determine a formula for the tax a person would pay with an adjusted
  gross income that is between $28,400 and $68,800

• Answer: 3910+0.25(x-28400)

				
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