Functions

1. Block 3
Functions

2. What is to be Learned?
• What a function is
• Different ways functions can be represented
• Meaning of words domain and range
• How to express functions

3. Functions are like Factories

4. Basic Function
Something goes in and comes out different
(usually!)
In Out+ 4
Domain Range

5. Basic Function
Something goes in and comes out different
(usually!)
In Out+ 4
Domain Range

6. Basic Function
In Out
5
-5
x
In Out+ 4
9
-1
x + 4

7. Basic Function
Domain Range
5
-5
x
In Out+ 4
9
-1
x + 4

8. Fancy Way of Writing
F(x) = x + 4
↑ ↑
Domain Range
F(7) ?
F(7) = 7 + 4
= 11
F of x

9. F(x) = 2x + 3 Domain { 1 , 3 , 5 }
Range?
F(1)?
F(1) = 2(1) + 3
= 5
F(3) = 9
F(5) = 13
Range { 5 , 9 , 13 }

10. Representing Functions

11. Table
X 1 2 3 4 5
F(x) 5 7 9 11 13
F(x) = 2x + 3

12. Graph
x
F(x)
just
like Y
f(x) = 2x + 3

13. Daft looking things
Domain Range
5 13
10 23
11 25
19 41
f(x) = 2x + 3

14. Definition
For every value of x in the domain, there is
exactly one value of f (or y) in the range

15. Domain Range

16. f(x) = 5x + 9 f(x + 3)?
f(x + 3) =

17. f(x) = 5x + 9 f(x + 3)?
f(x + 3) =

18. f(x) = 5x + 9 f(x + 3)?
f(x + 3) =

19. f(x) = 5x + 9 f(x + 3)?
f(x + 3) =

20. f(x) = 5x + 9 f(x + 3)?
f(x + 3) =
= 5x + 15 + 9
= 5x + 24
5 + 9x + 3( )x

21. f(x) = 3x – 2
f(x + 5) = 3
= 3x + 15 – 2
= 3x + 13
– 2x + 5( )
f(x + 5)?

22. f(x) = x2
f(x + 3) =
= (x + 3)(x + 3)
= x2
+ 3x + 3x + 9
= x2
+ 6x + 9
2x + 3( )
f(x + 3)?

23. Functions
In functions the domain values (usually x)
give one range value (usually f(x) or y)
Can be represented by formulae, graphs,
tables or daft diagrams.

24. f(x) = x2
+ 6
f(4) =
f(x + 3) =
42
+ 6
(x + 3)2
+ 6

25. g(x) = x2
+ 4x – 3
g(5) =
g(x – 7 ) =
52
+ 4(5) – 3
(x – 7)2
+ 4(x – 7) – 3

26. f(x) = 6x – 2
f(x + 4) = 6
= 6x + 24 – 2
= 6x + 22
– 2x + 4( )
f(x + 4)?
Key Question

27. Forbidden Domain Values!
Sums that do not work!!!!!
• Dividing by zero
• Square root of a negative

28. Applying to Functions
f(x) = 10
/x
Domain: x cannot equal zero
x = 0

29. f(x) = √x
Domain: x must not be negative
x ≥ 0

30. Sneakier
f(x) = 10
/x-3
Domain: x = 3
f(x) = √x – 5
Domain x ≥ 5

31. For some functions there are domain
values which are undefined
Ex f(x) = √x – 7
Domain x ≥ 7