PreCalculus 12
Date _________________
Unit 1: Function Transformations
1.3 Combining Transformations
−
=
( − ℎ) OR
=
( − ℎ) +
When applying multiple transformations the shape/orientation of the graph will be changed before its
position.
ie.
stretches & reflections – multiplication
before
translations – addition/subtraction
* also very important to factor the coefficient of
BEDMAS!
inside the function
Ex. Given the graph of ( )shown describe the
transformations that will be applied for each stated
transformed function. Give the mapping notation for each
and sketch the transformed graph.
a)
= 3 (2 )
10
9
8
7
6
5
4
3
2
1
-1
b)
= − (3 + 6) + 2
1
2
3
4
5
6
7
8
-1
5
4
3
2
1
-5
-4
-3
-2
-1
1
-1
-2
-3
-4
-5
2
3
4
5
Ex. Given the graph of ( ) shown describe the transformations that will be applied, state the mapping
notation and sketch ( ) = 2
1−
−1
6
5
( )=
4
3
2
1
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
Ex. The function ( ) =
is expanded vertically by a factor of 5, reflected in the -axis, compressed
horizontally by a factor of , translated 6 units right and 3 units down. Write the equation of the new
function ( ).
Ex. The graph of the function = ( ) represents a transformation of the graph of
Determine the equation of ( ) in function notation.
= ( ).
7
6
y=f(x)
5
4
3
2
1
-6
-5
-4
-3
-2
-1
1
2
3
4
-1
-2
-3
-4
-5
-6
-7
-8
-9
Practice: pg. 38/# 1 – 11, 13, 17, C3
y=g(x)
5
6