Download Transformations of ( ) fxx = KEY

Algebra 2
HS Mathematics
Unit: 06 Lesson: 01
Transformations of f ( x )  x KEY
WINDOW
Xmin= -9.4
Xmax= 9.4
Xscl= 1
Parent Function: f ( x ) = x
Use the given calculator settings to
graph each function below.
Ymin= -6.2
Ymax= 6.2
Yscl= 1
4
2
Endpoint:
(0,0)
Then tell how each new graph compares to the parent function
f ( x ) = x (shown at the right).
1. Function: f ( x )  x  3
Where is
the
Endpoint
?
2
2
4
2
4
6
2. Function: f ( x )  x  3
4
-2
-2
6
Where is
the
Endpoint
?
4
2
-2
(0,3)
2
4
6
(0 , -3)
How does the function compare to f ( x ) = x ?
Translated up 3 units
How does the function compare to f ( x ) = x ?
Translated down 3 units
3. Function: f ( x )  x  3
4. Function: f ( x )  x  3
Where is
the
Endpoint
?
4
2
-2
2
4
6
©2012, TESCCC
4
2
( -3 , 0 )
How does the function compare to f ( x ) = x ?
Translated to the left 3 units
Where is
the
Endpoint
?
-2
2
4
6
( 3 , 0)
How does the function compare to f ( x ) = x ?
Translated to the right 3 units
09/06/12
page 1 of 3
Algebra 2
HS Mathematics
Unit: 06 Lesson: 01
Transformations of f ( x )  x KEY
5. Function: f ( x )  ( x  4)  2
Where is
the
Endpoint
?
4
2
-2
6. Function: f ( x )  ( x  2)  1
2
4
Where is
the
Endpoint
?
4
2
-2
6
2
4
6
( -4 , 2 )
( 2 , -1 )
How does the function compare to f ( x ) = x ?
Translated to the left 4 units and up 2 units
How does the function compare to f ( x ) = x ?
Translated to the right 2 units and down 1 unit
7. Function: f ( x )  2.5 x
8. Function: f ( x )  0.6 x
Where is
the
Endpoint
?
4
2
-2
2
4
Where is
the
Endpoint
?
4
2
-2
6
2
4
6
(0,0)
(0,0)
How does the function compare to f ( x ) = x ?
Stretched vertically using a 2.5 scale factor
How does the function compare to f ( x ) = x ?
Compressed vertically using a 0.6 scale factor
9. Function: f ( x )   x
10. Function: f ( x ) = - 2 x
Where is
the
Endpoint
?
4
2
-2
2
4
2
-2
6
(0,0)
How does the function compare to f ( x ) = x ?
Reflected over the x-axis
©2012, TESCCC
Where is
the
Endpoint
?
4
2
4
6
(0,0)
)
How does the function compare to f ( x ) = x ?
Reflected over the x-axis, stretched vertically by a
scale factor of 2
09/06/12
page 2 of 3
Algebra 2
HS Mathematics
Unit: 06 Lesson: 01
Transformations of f ( x )  x KEY
Summary of Transformations:
For square root functions, there are four basic transformations:
Adding on the outside
Multiplying on the outside
Adding k translates the graph up
If a > 1, vertical stretch
Subtracting k translates the
If 0 < a < 1, vertical compression
graph down
If a < 0, reflects over x-axis
f ( x )  a  ( x  h)  k
Adding on the inside
Adding h translates the graph left
Subtracting h translates the
graph to the right
11. Write function rules for these graphs. Check them using a graphing calculator.
B. Take the function f ( x ) = x , stretch it to
be twice as tall, then translate it 3 units to
the left.
A. Take the function f ( x ) = x , reflect it over
the x-axis, and then translate it 5 units up.
4
4
2
2
-2
Function rule: y   x  5
©2012, TESCCC
2
4
-2
6
2
4
6
Function rule: y  2 ( x  3)
09/06/12
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