Math 107 quiz 3 | Mathematics homework help

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The quiz is worth 100 points.  Each problem is worth 5 points.

1.

 

For the given graph, please determine the intervals where the graph is

(a)  increasing, (b) decreasing, or (c) constant.

 

 

 

 

 

 

 

 

 

2.

  

Determine the intervals where the graph is increasing, and also any relative maxima or minima.

 

 

 

 

 

 

 

 

3.  (a)   The area of a rectangle formula is A = lw.  Suppose that 

             the width is 5 less than the length.   Expressarea as a

             function of the width.

 

 

 

 

 

 

 

      (b)   Use the function that you got from (a) to find the area

             when the width is 10 inches.   Please make sure to give

             an appropriate unit of area.

 

 

 

 

4.  A hot-air balloon rises straight up from the ground at a rate of 120 ft/min.

     The balloon is tracked from a rangefinder on the ground at point P, which is

     400 ft from the release point Q of the balloon.   Let d = the distance from the

     balloon to the rangefinder and t = the time, in minutes, since the balloon was

     released.   Express d as a function of t.   (HINT: Please use the Pythagorean

     Theorem which says   a2 + b2 = c2).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.    Graph the piecewise function given by

 

        

  

     Then, determine the domain and range.

 

 

 

 

 

 

 

6.       Given the function f( x ) = x3 – x + 20 and g( x ) = 10x2, find

           each of the following  (NOTE:  each part is independent from

           the other).   

 

 

(a)            (f + g)(x)

 

 

 

 

 

(b)            (g – f)(x)

 

 

 

 

 

(c)             (ff)(x)

 

 

 

 

 

 

(d)           (gf)(x)

 

 

 

 

 

 

(e)             (f/g)(x)

 

 

 

 

 

 

 

 

7.       Given the function f( x ) = x3 – x + 20 and g( x ) = 10x2, find

           each of the following  (NOTE:  each part is independent from

           the other).   

 

 

 

                    (a)     

 

 

 

 

 

 

 

                    (b)    

 

 

 

 

 

 

                        (c)    

 

 

 

 

 

 

 

8.   Given the revenue function, R(x) = 60x – .4x2 and the cost function,

      C(x) = 3x + 13, and using the fact that P(x) = R(x) – C(x), please find

(a)    P(x)

 

 

 

 

(b) P(10)

 

 

 

 

 

 

 

 

 

 

 

 

9.  Given that f( x ) = x2, please find the difference quotient,    .

 

 

 

 

 

 

 

10.  The graph of y = f( x ) is the first graph shown and  y = g( x ) is the graph

       shown just underneath that.  (No formulas are given.)   Please choose which  

       best describes  the relationship between the two graphs.    HINT:   Please find

       points on each of y = f( x ) and y = g( x ) and compare the points on y = f( x )

       and y = g( x ).

 

 

               

(a)   g( x ) = f( x + 1) – 2

(b) g( x ) = f( x – 1 ) + 2

(c)  g( x ) = f( x + 2 ) + 1

(d)g( x ) = f( x – 2 ) + 1

 

 

 

 

 11.   In the following sentence, please fill in each blank with

         either of the words “up”, “down”, “right”, or “left”.

 

                    The graph of y = | x + 7 | – 2  is the graph of y = | x | moved 

                     _______ 7 units and  ______ 2 units.  

 

12.  Given that (3, 4) and (1, -2) are points on the graph of y = f( x ), please

       list each of the corresponding points on the graph of y = -f( x ).

 

 

 

 

13.  Given that (3, 4) and (1, -2) are points on the graph of y = f( x ), please

       list each of the corresponding points on the graph of y = 4f( x ).

 

 

 

 

14.     Please feel free to use the graph of the equation or test algebraically to

          determine the kinds of symmetry that each of the following equations have.  

 

(a)    y = | 5x |

 

 

 

 

 

 

(b)   xy = 12

 

 

 

 

 

 

(c)   y = 1

 

 

 

 

 

 

 

                    (d)  x2 + y2 = 9

 

 

 

 

 

 

 

 

 

 

 

15.     Please feel free to use the graph of the equation or test algebraically to

          determine whether the following equation is an odd function, an even

          function, a function that is neither odd nor even, or a function that is both

         odd and even.            

 

(a)      y = | 5x |

 

 

 

 

 

 

(b)   xy = 12

 

 

 

 

 

 

(c)   y = 1

 

 

 

 

 

                    (d) 

 

 

 

 

 

16.  Find a point that is symmetric to (1, 2) with respect to the x-axis,

      y-axis, and the origin.

 

 

 

 

FOR #17 AND #18, FIND THE VARIATION CONSTANT AND AN

EQUATION OF VARIATION FOR THE GIVEN SITUATION.

  

17.  y varies directly as x, and y = .1 when x = .2.

 

 

 

18.  y varies inversely as x, and y = .2 when x = 35.

 

 

 

 

19.  The weight M of an object on the moon varies directly as its weight

        E on earth.  A person weighs 169.76 lbs on earth weighs 28.86 lbs

        on the moon.  How much would a 241.76-lb person weigh on the

       moon?

 

 

 

 

20.  The stopping distance d of a car after the brakes have been applied

       varies directly as the square of the speed r.   If a car traveling

       60 mph can stop in 200 ft, how fast can a car travel and will stop in

 

       72 ft?

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