Function Graphs

1. Block 3
Function Graphs

2. 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)

3. Handy Graphs To know
f(x) = x2

4. Handy Graphs To know
f(x) = x3

5. The Rules
y = f(x)
(-3 , 4)
( 2 , 1)
y = f(x) + 2
(-3 , 6)
( 2 , 3)
2

6. The Rules
y = f(x)
(-3 , 4)
( 2 , 1)
y = f(x – 2)
(-1 , 4)
( 4, 1)
2

7. The Rules
y = f(x)
(-3 , 4)
( 2 , 1)
y = -f(x)
(-3 , -4)
( 2, -1)
Reflects in
x axis

8. The Rules
y = f(x)
(-3 , 4)
( 2 , 1)
y = f(-x)
(3 , 4)
( -2, 1)
Reflects in
y axis

9. Y = 2f(x) and y = f(2x)
Remember Trig Graphs
f(x) = sinx
f(x) = 2sinx
Graph “stretches”

10. Y = 2f(x) and y = f(2x)
Remember Trig Graphs
f(x) = sinx
f(x) = sin2x
Graph Squashes

11. Function Graph Families
Given graph y = f(x) we can sketch family
graphs by following these rules
y = f(x) – 2
y = f(x + 2)
y = -f(x)
y = f(-x)
y =2f(x)
y = f(2x)
2 down
2 to left
reflects in x axis
reflects in y axis
stretches
squashes
*
*
* Think of trig graphs

12. sketch y = 3 – f(x)
y = f(x)
Ex
(3 , -1)
2
Cunningly change to y = -f(x) + 3
(3 , 1)
-2
y = -f(x)
y = -f(x) + 3
(3 , 4)
1

13. y = f(x)(-2 , 5)
( 1 , 2)
y = f(x – 2)
(0 , 5)
(3 , 2)
Key Question
Sketch y = f(x – 2) + 1 showing new key points
y = f(x – 2) + 1
(0 , 6)
(3 , 3)