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Unit	
  6	
  Review	
  Answers	
  
1.	
  	
  Decay	
   2.	
  	
  Growth	
   3.	
  	
  Growth	
   4.	
  	
  Decay	
  	
   	
  
5.	
  	
   Function	
   	
   	
   Inverse	
  
	
   	
  
Domain	
  –	
  All	
  Reals	
   	
   Domain	
  –	
  x	
  >	
  0	
  
Range	
  :	
  	
  y	
  >0	
   	
   	
   Range	
  –	
  All	
  Reals	
  
	
   	
   	
   	
   Yes	
  is	
  a	
  function	
  
	
  
	
  
6.	
  	
  Function	
   	
   	
   	
   	
   	
   Inverse	
  
	
  
Domain:	
  	
  All	
  Reals	
   	
   	
   	
   Domain:	
  	
  x	
  >	
  -­‐2	
  
Range:	
  	
  y	
  >	
  -­‐2	
   	
   	
   	
   	
   Range:	
  	
  All	
  Reals	
  
	
   	
   	
   	
   	
   	
   Yes	
  is	
  a	
  function	
  
	
  
	
  
	
  
7.	
  	
  Function	
   	
   	
   	
   	
   	
   	
   Inverse	
  
Domain:	
  	
  All	
  Reals	
   	
   	
   	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  Domain:	
  	
  x	
  >	
  -­‐2	
  
Range:	
  	
  y	
  >	
  -­‐2	
   	
   	
   	
   	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   Range:	
  All	
  Reals	
  
	
   	
   	
   	
   	
   	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   Yes	
  is	
  a	
  function	
  
	
  
8.	
  	
  up	
  12	
   9.	
  	
  Right	
  8	
   10.	
  	
  Left	
  2,	
  up	
  4	
  	
   11.	
  	
  log! 81 = 4	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  12.	
  	
  log!
!
2 = −1	
  
13.	
  	
  log! 1 = 0	
  	
  	
  	
  	
  	
  	
  	
  14.	
  	
  10!
= 100	
  	
  	
  	
  	
  	
  	
  15.	
  	
  8!!
=
!
!"
	
  	
  	
  	
  	
  16.	
  	
  27
!!
! =
!
!
	
  	
  	
  	
  	
  	
  17.	
  	
  0.9176	
  	
  	
  	
  	
  	
  	
  	
  18.	
  	
  1	
  
19.	
  	
  1.5937	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  20.	
  	
  -­‐3	
  	
  	
  	
  	
  	
  21.	
  	
  -­‐1/2	
  	
  	
  	
  	
  	
  	
  	
  22.	
  	
  3/2	
  	
  	
  	
  	
  	
  	
  	
  23.	
  	
  2.5646	
  	
  	
  	
  	
  	
  	
  24.	
  	
  1.5279	
  	
  	
  	
  	
  25.	
  	
  0.4909	
  
26.	
  	
  -­‐3.6837	
  	
  	
  	
  	
  	
  	
  	
  27.	
  	
  10.8817	
  	
  	
  	
  	
  	
  	
  28.	
  	
  0.1521	
  	
  	
  	
  	
  29.	
  	
  Up	
  2,	
  	
  g(x)	
  =	
  2x
-­‐6	
  	
  	
  	
  	
  	
  	
  
30.	
  	
  vertical	
  shrink	
  of	
  ½,	
  	
  down	
  3	
  	
  	
  	
  	
  	
   𝑔 𝑥 = 2(
!
!
)!
− 2	
  	
  	
  	
  	
  	
  	
  	
  	
  
31.	
  	
  1992	
  –	
  2,	
  521,135.366	
  people	
  	
  	
  	
  	
  	
  	
  2006	
  –	
  2979362.449	
  people	
  	
  	
  	
  	
  	
  32.	
  	
  12.01	
  months	
  
33.	
  	
  32.17	
  years	
  	
  	
  	
  	
  34.	
  	
  $20550.63	
  	
  	
  	
  	
  	
  	
  	
  35.	
  	
  $81,	
  920.00	
  	
  	
  	
  (note,	
  it	
  doubles	
  every	
  year,	
  not	
  every	
  3	
  years)	
  
	
   	
  
	
  
x	
   y	
  
-­‐2	
   16	
  
-­‐1	
   8	
  
0	
   4	
  
1	
   2	
  
2	
   1	
  
X	
   Y	
  
16	
   -­‐2	
  
8	
   -­‐1	
  
4	
   0	
  
2	
   1	
  
1	
   2	
  
x	
   y	
  
-­‐2	
   -­‐1.5	
  
-­‐1	
   -­‐1	
  
0	
   0	
  
1	
   2	
  
2	
   6	
  
X	
   Y	
  
-­‐1.5	
   -­‐2	
  
-­‐1	
   -­‐1	
  
0	
   0	
  
2	
   1	
  
6	
   2	
  
x	
   y	
  
-­‐2	
   -­‐1.97	
  
-­‐1	
   -­‐1.875	
  
0	
   -­‐1.5	
  
1	
   0	
  
2	
   6	
  
X	
   Y	
  
-­‐1.97	
   -­‐2	
  
-­‐1.875	
   -­‐1	
  
-­‐1.5	
   0	
  
0	
   1	
  
6	
   2	
  

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Unit 6 review answers

  • 1. Unit  6  Review  Answers   1.    Decay   2.    Growth   3.    Growth   4.    Decay       5.     Function       Inverse       Domain  –  All  Reals     Domain  –  x  >  0   Range  :    y  >0       Range  –  All  Reals           Yes  is  a  function       6.    Function             Inverse     Domain:    All  Reals         Domain:    x  >  -­‐2   Range:    y  >  -­‐2           Range:    All  Reals               Yes  is  a  function         7.    Function               Inverse   Domain:    All  Reals                                                                            Domain:    x  >  -­‐2   Range:    y  >  -­‐2                                     Range:  All  Reals                                   Yes  is  a  function     8.    up  12   9.    Right  8   10.    Left  2,  up  4     11.    log! 81 = 4                      12.    log! ! 2 = −1   13.    log! 1 = 0                14.    10! = 100              15.    8!! = ! !"          16.    27 !! ! = ! !            17.    0.9176                18.    1   19.    1.5937                      20.    -­‐3            21.    -­‐1/2                22.    3/2                23.    2.5646              24.    1.5279          25.    0.4909   26.    -­‐3.6837                27.    10.8817              28.    0.1521          29.    Up  2,    g(x)  =  2x -­‐6               30.    vertical  shrink  of  ½,    down  3             𝑔 𝑥 = 2( ! ! )! − 2                   31.    1992  –  2,  521,135.366  people              2006  –  2979362.449  people            32.    12.01  months   33.    32.17  years          34.    $20550.63                35.    $81,  920.00        (note,  it  doubles  every  year,  not  every  3  years)         x   y   -­‐2   16   -­‐1   8   0   4   1   2   2   1   X   Y   16   -­‐2   8   -­‐1   4   0   2   1   1   2   x   y   -­‐2   -­‐1.5   -­‐1   -­‐1   0   0   1   2   2   6   X   Y   -­‐1.5   -­‐2   -­‐1   -­‐1   0   0   2   1   6   2   x   y   -­‐2   -­‐1.97   -­‐1   -­‐1.875   0   -­‐1.5   1   0   2   6   X   Y   -­‐1.97   -­‐2   -­‐1.875   -­‐1   -­‐1.5   0   0   1   6   2