Worksheet: Iterated Functions

In this worksheet, we will practice iterating a function to recursively generate a sequence.

Q1:

Given an initial value 𝑥, we can iterate a function using the recursive formula 𝑥=𝑓(𝑥).

Find 𝑥 given the function 𝑓(𝑥)=3𝑥2 with initial value 𝑥=2.

Q2:

We can define a sequence 𝑥,𝑥,𝑥, using the recursive formula 𝑥=𝑓(𝑥) for some function 𝑓 and initial value 𝑥.

Write the first 5 terms of the sequence generated by 𝑓(𝑥)=83𝑥, 𝑥=11.

  • A 1 1 , 8 , 1 6 , 5 6 , 1 6 0
  • B 1 1 , 4 1 , 1 1 5 , 3 3 7 , 1 , 0 1 9
  • C 1 1 , 4 1 , 1 1 5 , 3 5 3 , 1 , 0 5 1
  • D 1 1 , 2 5 , 8 3 , 2 4 1 , 7 3 1
  • E 1 1 , 4 1 , 1 1 5 , 3 5 3 , 1 , 0 5 1

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