Function Graph Movements
What is to be Learned
• How to sketch images of given function
graph f(x) under rules such as




f(x) + 2
f(x + 2)
-f(x)
f(-x)
Will also have peek at y = 2f(x) and y = f(2x)
Handy Graphs To know
f(x) = x2
Handy Graphs To know
f(x) = x3
The
(-3
, 6)
Rules
y = f(x)
y = f(x) + 2
(-3 , 4) ( 2 , 3)
2
( 2 , 1)
The Rules
y = f(x)
y = f(x – 2)
(-3 , 4)(-1 , 4)
2
( 2 , 1)( 4, 1)
The Rules
y = f(x)
y = -f(x)
Reflects in
x axis
(-3 , 4)
( 2 , 1)
( 2, -1)
(-3 , -4)
The Rules
y = f(x)
y = f(-x)
Reflects in
y axis
(-3 , 4)
(3 , 4)
( -2, 1) ( 2 , 1)
Y = 2f(x) and y = f(2x)
Remember Trig Graphs
f(x) = 2sinx
f(x) = sinx
Graph “stretches”
Y = 2f(x) and y = f(2x)
Remember Trig Graphs
f(x) = sin2x
f(x) = sinx
Graph Squashes
Function Graph Families
Given graph y = f(x) we can sketch family
graphs by following these rules
y = f(x) – 2 2 down
y = f(x + 2)
2 to left
y = -f(x)
reflects in x axis
y = f(-x)
reflects in y axis
y =2f(x) *
stretches
squashes
y = f(2x) *
* Think of trig graphs
Ex
sketch y = 3 – f(x)
Cunningly change to y = -f(x) + 3
(3 , 4)
2
1
-2
(3 , 1)
(3 , -1)
y = f(x)
y = -f(x) + 3
y = -f(x)