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MCR3U
TRANSFORMATIONS ON EXPONENTIAL GRAPHS
Given the base graph y  b x , transformations on this function are as such:
a) Vertical Stretches and Reflections about the x-axis: y  a(b) x where a  R
eg. Graph y  2 x , y  3(2 x ) and y  21 (2 x ) on the grid below.
What is the effect of “a” on the graph of y  a(b) x compared to the graph of y  b x ?
b) Horizontal and Vertical Translations
x
Graph
1
1
y  , y 
2
2
x2
y  b x  d  c , c, d  R
1
and y   
2
x 3
 1 on the grid below
What is the effect of “c”& “d” on the graph of y  b x  d  c compared to the graph of y  b x ?
2
MCR3U
TRANSFORMATIONS ON EXPONENTIAL GRAPHS
We notice that the graphs follow the same transformation results as we found when dealing
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with quadratic y  x 2 , square root y  x , reciprocal y  or any other type of function we
x
have been transforming in previous grades and chapters.
To continue some practice/investigation, graph the following:
Identify the base graph and state the transformations used
a) y  3 x 1  2
Base graph is
_______
Transformations used:___________________________________
Graph using transformations:
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MCR3U
1
b) y   
3
TRANSFORMATIONS ON EXPONENTIAL GRAPHS
2x
Base graph is
_______
Transformations used:___________________________________
Graph using transformations:
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MCR3U
c) y  2 3 x
TRANSFORMATIONS ON EXPONENTIAL GRAPHS
Base graph is
_______
Transformations used:___________________________________
Graph each using transformations:
Describe the roles of the parameters of a, k, d, c in the function
y  a f k ( x  d ) c in terms of transformations on the graph of f ( x )  b x