# Lesson Worksheet: Iterated Functions Mathematics

In this worksheet, we will practice using an iterative formula to approximate the roots of an equation.

Q1:

Given an initial value , we can iterate a function using the recursive formula .

Find given the function with initial value .

Q2:

We can define a sequence using the recursive formula for some function and initial value .

Write the first 5 terms of the sequence generated by , .

• A
• B
• C
• D
• E

Q3:

We can iterate a function using the recursive formula . Find the positive fixed point.

• A
• B1
• C
• D
• E2

Q4:

We can iterate the function using the recursive formula with initial value . Find .

Q5:

We can iterate the function using the recursive formula with initial value . Find .

Q6:

True or False:

The recursive formula of the function can produce an even number with initial value .

• AFalse
• BTrue

Q7:

Michael saves \$100 every month. The savings of the current month can be calculated with the recursive function , where is the savings of the previous month. Find the savings of the 4th month given that his initial savings were \$1,000.

Q8:

We can iterate the function using the recursive formula with initial value . Find .

Q9:

We can iterate the function using the recursive formula with initial value . Find to the nearest two decimal places.

Q10:

We can iterate the function using the recursive formula with initial value . Find .