Math 2
Chapter 3.5: Function Transformations
Name _____________________
y
Cube Function
f ( x)
x
x3
y
y
x3
( x, y )
-2
-1
x
0
1
2
Vertical Shift Up
f ( x)
x
x
3
y
y
2
x3
2
y
( x, y )
f ( x)
-2
k shifts graph
-1
(Add 2 to each y-coordinate)
0
x
1
2
Vertical Shift Down
f ( x)
x
-2
x3
2
y
x3 2
y
y
( x, y )
f ( x)
k shifts graph
-1
(Subtract 2 from each y-coordinate)
0
1
2
x
y
Horizontal Shift Left
f ( x)
x
( x 2)3
y
(x 2)3
y
( x, y )
f (x
-4
k ) shifts graph
-3
(Subtract 2 from each x-coordinate)
x
-2
-1
0
Horizontal Shift Right
f ( x)
x
( x 2)
y
y
3
(x 2)3
y
( x, y )
f (x
0
k ) shifts graph
1
(Add 2 to each x-coordinate)
2
x
3
4
Stretching Vertically
f ( x)
x
-2
y
2 x3
y
2x 3
y
( x, y )
af (x) for a 1 stretches the
graph vertically
-1
0
1
2
(Multiply each y-coordinate by 2)
x
Compressing Vertically
1 3
f ( x)
x
2
y
x
1 3
y
x
2
-2
y
( x, y )
af (x) for 0
a 1 compresses
the graph vertically
-1
x
0
(Multiply each y-coordinate by ½)
1
2
Compressing Horizontally
f ( x)
x
( 2 x)
y
y
3
(2 x)3
y
( x, y )
f (ax) for a 1 compresses the
-1
graph horizontally
-1/2
0
x
(Multiply each x-coordinate by ½)
1/2
1
Stretching Horizontally
1
f ( x) ( x)3
2
x
1
y ( x)3
2
-4
y
y
( x, y )
f (ax) for 0
a 1 stretches
the graph horizontally
-2
x
(Multiply each x-coordinate by 2)
0
2
4
y
Reflection About the X-Axis
f ( x)
x
x3
y
y
x3
( x, y )
f (x) flips the graph over the
-2
x-axis
-1
x
0
(Multiply each y-coordinate by -1)
1
2
y
Reflection About the Y-Axis
f ( x)
x
( x) 3
y
( x)3
y
( x, y )
f ( x) flips the graph over the
-2
y-axis
-1
x
0
1
(Multiply each x-coordinate by -1)
2
Why does
f (x) and f ( x) have the same graph?
Apply What You know About Transformations to Graph Without Plotting Points
f ( x)
x 1 2
f ( x)
( x 1)3 3
f ( x) x 2 3
y
y
x
y
x
x