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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

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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