ADVANCED MATH
LESSONS 3-5: THE GRAPH SCALE-CHANGE THEOREM WORKSHEET
NAME: ______________________
DATE: ______________________
PERIOD: _____
GENERAL DIRECTIONS: Read each problem/situation carefully. Show all of your work to receive
partial credit.
1.
Multiplying by 5 gives the same answer as dividing by ___________.
2.
Multiplying by 0.75 gives the same answer as dividing by __________.
3.
Make a general statement which summarizes questions 1 and 2 above (generalize to account
for multiplying by any number).
____________________________________________________________________
4.
Find the scale change S which shrinks a graph horizontally
5) __________________
1
with a factor of and stretches it vertically with a factor of 8.
6
5.
Describe the effect of the scale change S : (x, y)  (3x,2y) on a graph.
____________________________________________________________________
6.
Describe the effect of the scale change S : (x, y)  (3x,2y) on a graph.
____________________________________________________________________
7.
x

Consider the parabola y  x2 . Let S(x, y)   ,3y  .
2

A) Find the image of (-3,9), (0,0) and (½ , ¼) under S.
A) __________________
B) Write the equation for the image under S.
B) __________________
8.
Consider the function y  x . Let S(x, y)  3x, y  .
A) Find the image of (-6,6), (3,3) and (6,6) under S.
A) __________________
B) Write the equation for the image under S.
B) __________________
C) Graph the function and its image under transformation S.
D) Describe the effect transformation S has on the graph of the function y  x .
____________________________________________________________________
9.
x y
The graph of a function f is shown below. Graph the image f' under S(x, y)   , 
2 3
A) Find the x-intercepts of the image f’. __________________
B) Find the y-intercept of the image f’.
__________________
C) Find the coordinates where the y-value of the image of f
reaches its:
maximum
_______________
minimum
_______________
10.
Give a rule for a scale change that maps f to g for each graph below.
Rule: ____________________
11.
Rule: ____________________
Given triangle ABC and its image below.
A) What type of transformation occurred to produce A'B'C' ? A) __________________
B) Write the rule for the transformation.
12.
B) __________________
Describe two different transformations S1 and S2 which map the graph of y  x2 onto
the graph of y 
9 2
x .
4
_________________________
_________________________
13.
Scale changes of parabolas can be considered as horizontal scale changes or vertical
scale changes or both. Refer to the graphs below.
Rule for Horizontal Scale Change
mapping f onto g:
______________________________
Rule for Vertical Scale Change
mapping f onto g:
______________________________
14.
15.
16.
Given the function y  125x3 .
a.
Write this as a vertical scale change:
S(x,y)=__________________
b.
Write this as a horizontal scale change.
S(x,y)=__________________
Given the function y  49x2 .
a.
Write this as a vertical scale change:
S(x,y)=__________________
b.
Write this as a horizontal scale change.
S(x,y)=__________________
Write the equation for the image of y  x under the

y
transformation S(x, y)   5x,  .
2

16) ______________________