1. All pupils are confident with function notation including:
L.O.
All pupils are confident with function notation including:
domain and range
composite functions
inverse functions
rational functions

2. Starter:

3. Starter:

4. All pupils are confident with function notation including:
L.O.
All pupils are confident with function notation including:
domain and range
composite functions
inverse functions
rational functions

5. Use this image to write a description of domain and range

6. Find the domain and the range of these functions:
domain and range
Find the domain and the range of these functions:

7. All pupils are confident with function notation including:
L.O.
All pupils are confident with function notation including:
domain and range
composite functions
inverse functions
rational functions

8. What does this diagram represent?
Main 2:
composite functions
What does this diagram represent?

9. Main 2:
composite functions
An example:

10. Work through the questions on the other board…
Main 2:
composite functions
Work through the questions on the other board…

11. All pupils are confident with function notation including:
L.O.
All pupils are confident with function notation including:
domain and range
composite functions
inverse functions
rational functions

12. What are inverse functions?
Main 3:
inverse functions
What are inverse functions?

13. Main 3: An Example: How was it found?
inverse functions
An Example:
How was it found?

14. Find the inverses of these equations
Main 3:
inverse functions
Find the inverses of these equations

15. Main 3:
inverse functions
What happens to the domain and the range of the original function when it is inversed?

16. Main 3:
inverse functions
What happens to the graph of the original function when it is inversed?

17. All pupils are confident with function notation including:
L.O.
All pupils are confident with function notation including:
domain and range
composite functions
inverse functions
rational functions

18. What are rational functions?
Main 4:
rational functions
What are rational functions?
Hint: what are rational numbers?
Functions that can be written as a fraction.

19. Write a rational function on your wipeboard.
Main 4:
rational functions
Write a rational function on your wipeboard.

20. There are so many thing you can find with rational functions!
Main 4:
rational functions
There are so many thing you can find with rational functions!
Standards: You need to be able to factorise, find the asymptotes, find any points of intersection, sketch the graph.
Highers: You need to be able to do all of the above but as part of a deeper question

21. factorise, find the asymptotes, find any points of intersection, sketch the graph.
Main 4:
rational functions

22. factorise, find the asymptotes, find any points of intersection, sketch the graph.
Main 4:
rational functions
A few lessons ago we looked at finding the domain and the range for these functions:
𝒇 𝒂 = 𝟒𝒂 𝟑𝒂−𝟏 and 𝒇 𝒙 = 𝟑−𝒙 𝟒+𝒙

23. factorise, find the asymptotes, find any points of intersection, sketch the graph.
Main 4:
rational functions

24. find any points of intersection
factorise, find the asymptotes, find any points of intersection, sketch the graph.
Main 4:
rational functions
𝒇 𝒂 = 𝟒𝒂 𝟑𝒂−𝟏 and 𝒇 𝒙 = 𝟑−𝒙 𝟒+𝒙
Ext.
find any points of intersection
sketch the graph

25. Main 4:
rational functions

26. Notice the link with reciprocal functions:
Main 4:
rational functions
Notice the link with reciprocal functions:

27. All pupils are confident with function notation including:
L.O.
All pupils are confident with function notation including:
domain and range
composite functions
inverse functions
rational functions