Functions Review

Choose two numbers from 1 to 8 and two letters from A to H Let the numbers be functions f(x) and g(x) And the letters be corresponding transformations of these functions

𝐴 𝑥 = 𝑥 2 +2 𝑓 𝑥+3 𝐴 𝑥 = 𝑥 2 +𝑥 𝑓 2𝑥 𝐴 𝑥 = −𝑥 2 2𝑓 𝑥 𝐴 𝑥 = 1 𝑥 𝑓 𝑥−2 FUNCTION TRANSFORMATION 𝐴 𝑥 = 𝑥 2 +2 𝐴 𝑥 = 𝑥 2 +𝑥 𝐴 𝑥 = −𝑥 2 𝐴 𝑥 = 1 𝑥 𝐴 𝑥 = 2𝑥 2 −1 𝐴 𝑥 = 1 𝑥 +3 𝐴 𝑥 = 3−𝑥 2 𝐴 𝑥 = 1 𝑥+1 𝑓 𝑥+3 𝑓 2𝑥 2𝑓 𝑥 𝑓 𝑥−2 𝑓 𝑥 +2 𝑓 𝑥 −1 𝑓 1 2 𝑥 𝑓 𝑥+2

Sketch graphs of each function state the domain and inverse and show key points 2) Find the inverse of each function 3) Sketch graphs of each inverse function state the domain and inverse and show key points 4) Apply the transformations to each function algebraically 5) Sketch graphs of each transformed function state the domain and inverse and show key points 6) Work out the composite functions fg(x) and gf(x) state the domain and inverse of composite functions

Sketch graphs of each function Example 𝑓 𝑥 = 𝑥 2 +2 𝑔 𝑥 = 1 𝑥 +3 A: 𝑓 𝑥+3 F: 𝑔 𝑥 −1 Sketch graphs of each function state the domain and inverse and show key points

2) Find the inverse of each function Example 𝑓 𝑥 = 𝑥 2 +2 𝑔 𝑥 = 1 𝑥 +3 2) Find the inverse of each function x= 𝑦 2 +2 x= 1 𝑦 +3 𝑦 2 =𝑥−2 1 𝑦 =𝑥−3 𝑦=+ 𝑥−2 𝑦= 1 𝑥−3 𝑓 −1 (𝑥)= 𝑥−2 𝑔 −1 𝑥 = 1 𝑥−3

3) Sketch graphs of each inverse function Example 𝑓 𝑥 = 𝑥 2 +2 𝑔 𝑥 = 1 𝑥 +3 3) Sketch graphs of each inverse function state the domain and inverse and show key points 𝑓 −1 (𝑥)= 𝑥−2 𝑔 −1 𝑥 = 1 𝑥−3

4) Apply the transformations to each function algebraically Example 𝑓 𝑥 = 𝑥 2 +2 𝑔 𝑥 = 1 𝑥 +3 A: 𝑓 𝑥+3 F: 𝑔 𝑥 −1 4) Apply the transformations to each function algebraically 𝑔 𝑥 −1 = 1 𝑥 +3 −1 𝑓 𝑥+3 = (𝑥+3) 2 +2 𝑓 𝑥+3 = 𝑥 2 +6𝑥+11 𝑔 𝑥 −1 = 1 𝑥 +2

5) Sketch graphs of each transformed function Example 𝑓 𝑥 = 𝑥 2 +2 𝑔 𝑥 = 1 𝑥 +3 5) Sketch graphs of each transformed function state the domain and inverse and show key points 𝑓 𝑥+3 = 𝑥 2 +6𝑥+11 𝑔 𝑥 −1 = 1 𝑥 +2

Example 𝑓 𝑥 = 𝑥 2 +2 𝑔 𝑥 = 1 𝑥 +3 6) Work out the composite functions fg(x) and gf(x) state the domain and inverse of composite functions 𝑓 𝑔(𝑥) = 𝑓 1 𝑥 +3 𝑔 𝑓(𝑥) = 𝑓 𝑥 2 +2 = 1 𝑥 2 +2 +3 = 1 𝑥 +3 2 +2 DOMAIN: 𝑥∈ℛ RANGE: graph it to see = 1 𝑥 2 + 6 𝑥 +11 DOMAIN: 𝑥≠0, 𝑥∈ℛ RANGE: graph it to see

END