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.

  • A11,8,16,56,160
  • B11,41,115,337,1,019
  • C11,41,115,353,1,051
  • D11,25,83,241,731
  • E11,41,115,353,1,051

Q3:

We can iterate the function 𝑓(𝑥)=|52𝑥| using the recursive formula 𝑥=𝑓(𝑥) with initial value 𝑥=8. Find 𝑥.

Q4:

We can iterate a function 𝑓(𝑥)=𝑥2+1𝑥 using the recursive formula 𝑥=𝑓(𝑥). Find the positive fixed point.

  • A22
  • B1
  • C12
  • D2
  • E2

Q5:

We can iterate the function 𝑓(𝑥)=𝑥+𝑥+1 using the recursive formula 𝑥=𝑓(𝑥) with initial value 𝑥=0. Find 𝑥.

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