Transformations-Combinations-WS-Student-Answer-Key

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					Honors Math 1 Transformations – Combinations WS Answer Key Name__________
                                               y
                                                                              f(x)
                                                                              f[(1/2)x]
                                          6
                                                                              1/3 f[(1/2)x]
                                                                              -1/3 f[(1/2)x]
                                          4                                   -1/3 f[(1/2)(x - 2)]



                                          2


                                                                                                                           x
       -8        -6            -4   -2                  2              4      6           8             10          12



                                          -2
                                                                                              1. Sketch the following
                                                                                              on the same grid,
                                                                                              using different colors and
                                                                                              clear labels for each:
                                          -4
                                                                                                   1 
                                                                                              a) f  x 
                                                                                                   2 
                                          -6                                                     1 1 
                                                                                              b) f  x 
                                                                                                 3 2 
                                                                                                 1  1 
                                          -8                                                  c)    f  x
                                                                                                 3 2 
                                                                                                 1  1           
                                                                                              d)     f  ( x  2) 
                                         -10                                                      3 2            




a) horizontal dilation of f(x) by a factor of 2              b) vertical dilation of f(½ x) by a factor of 1
                                                                                                                                   3
c) reflection of 1 f(½ x) over the x-axis                   d) horizontal translation of – 1 f(½ x) by +2 units
                      3                                                                                      3
                                                    y 2. Sketch the following on the same grid,
                                                      using different colors and clear labels for each:
                                                     2 g  3( x  3)   4
                                                     You may wish to do this one step at a time.
                                               8     If so clearly label/identify each step, and the
                                                     final answer.


                                               6



                                               4



                                               2



                                                                                                                               x
            -6            -4        -2                             2              4               6                8

                                                                                                  g(x)
                                               -2                                                 g(3x)
                                                                                                  g(-3x)
                                                                                                  2g(-3x)
                                                                                                  2g[-3(x + 3)] - 4
                                               -4




                                               -6
                                                                  y
                                                             18

                                                             16
3.                                                           14
 f(x)=x^2   f(x) = x2
                                                             12
 a)         2f(x) = 2x2
                                                             10
 b)         -2f(x) = -2x2
 c)         -2f(x + 3) = -2(x + 3) 2                          8
 d)         -2f(x + 3) + 4 = -2(x + 3) 2 + 4                  6

                                                              4

                                                              2
                                                                                                                x
        -10         -8         -6        -4        -2                      2            4       6       8
                                                             -2

                                                             -4

                                                             -6

                                                             -8

                                                         -10

                                                         -12

                                                         -14

                                                         -16

                                                         -18


a) vertical dilation of f(x) = x2 by a factor of 2   b) reflection of 2f(x) = 2x2 over the x-axis
                                           2
c) horizontal translation of –2f(x) = –2x by –3 units
d) vertical translation of –2f(x + 3) = –2(x + 3)2 by 4 units

                                                                                    y
                                                                               14

                                                                               12
4.                                                                             10
f(x)=x^2                                                                       8
g(x) =         ½x   2
                                                                               6
h(x) =         -½ x2                                                           4
k(x) =         -½ (x - 2)2
                                                                               2
m(x) =         -½ (x - 2)2 - 5                                                                                  x
  -14         -12        -10        -8        -6        -4            -2                    2       4       6
                                                                               -2

                                                                               -4

                                                                               -6

                                                                               -8

                                                                           -10

                                                                           -12


a) vertical dilation of f(x) by a factor of ½                 b) reflection of g(x) over the x-axis
c) horizontal shift of h(x) by +2 units                       d) vertical shift of k(x) by –5 units

				
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