Functions
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
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?
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?
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?
Ten questions Domain Odd Neither
1 of 10 What type of function? Even Even Odd Neither
2 of 10 What type of function? Even Odd Neither Neither
3 of 10 What type of function? Even Odd Odd Neither
4 of 10 What type of function? Even Odd Odd Neither
5 of 10 What type of function? Even Even Odd Neither
6 of 10 What type of function? Even Odd Neither Neither
7 of 10 What type of function? Even Odd Odd Neither
8 of 10 What type of function? Even Even Odd Neither
9 of 10 What type of function? Even Odd Neither Neither
10 of 10 What type of function? Even Odd Odd Neither
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)
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
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 –
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