1. Functions

2. Starter Functions KUS objectives
BAT understand definition of a function as a one to one mapping
BAT recognise odd and even functions
BAT state the domain and range of functions
Starter

3. Notes Odd and Even functions
A mapping represents an even function if 𝑓 𝑥 = 𝑓 −𝑥
A mapping represents an odd function if 𝑓 𝑥 = −𝑓 −𝑥
What transformations represents an even / odd function?
even function: Reflection of positive y values in the y-axis
odd function: Rotation of positive y value 180 about centre (0, 0)
Can you think of any functions that are even / odd?

4. Even functions: f(x) = f(-x) Can you think of any? Notes Think Pair
share
Even functions:
f(x) = f(-x)
Can you think of any?

5. Odd functions: f(x) = - f(-x) Can you think of any? Notes Think Pair
share
Odd functions:
f(x) = - f(-x)
Can you think of any?

6. Ten questions
Domain
Odd
Neither

7. 1 of 10
What type of function?
Even
Even
Odd
Neither

8. 2 of 10
What type of function?
Even
Odd
Neither
Neither

9. 3 of 10
What type of function?
Even
Odd
Odd
Neither

10. 4 of 10
What type of function?
Even
Odd
Odd
Neither

11. 5 of 10
What type of function?
Even
Even
Odd
Neither

12. 6 of 10
What type of function?
Even
Odd
Neither
Neither

13. 7 of 10
What type of function?
Even
Odd
Odd
Neither

14. 8 of 10
What type of function?
Even
Even
Odd
Neither

15. 9 of 10
What type of function?
Even
Odd
Neither
Neither

16. 10 of 10
What type of function?
Even
Odd
Odd
Neither

17. WB7 Draw a sketch of the function defined by 𝑓 𝑥 = 6 𝑥+1 , x−1
State it’s domain and range
Is f(x) an odd function? Give a reason for your answer
Domain 𝑥𝜖𝑅 𝑥≠−1
Range 𝑦 𝜖 𝑅 𝑦≠0
NOT an odd function
e.g. 𝑓 2 =2
𝑓 −2 =−6 Or
“𝑓 𝑥 ≠−𝑓(−𝑥)

18. WB8
Determine whether the following functions are odd, even or neither: 1. 3. 5. 7. 9.
11. 2. 4. 6. 8.
10.
12.
Use a graph package to check / investigate

19. One thing to improve is –
KUS objectives BAT understand definition of a function as a one to one mapping
BAT recognise odd and even functions
BAT state the domain and range of functions
self-assess
One thing learned is –
One thing to improve is –

20. END