For this example, use the function 1 () 1 2 fx x = + and an initial value of 4. Note that with each successive iteration, you can use the previous output as your new input
to the function.
• 1 (4) 4 1 3 2 f = ⋅+=
• 2 1 (4) (3) 3 1 2.5 2 f f = = ⋅+=
• 3 1 (4) (2.5) 2.5 1 2.25 2 f f = = ⋅ +=
Questions
3. What happens to the value of the function as the number of iterations
increases?
4. Choose an initial value that is less than zero. What happens to the value of
the function as the number of iterations increases?
5. Come up with a new linear function that has a slope that falls in the range
−< < 1 0 m . Choose two different initial values. For this new linear function,
what happens to the function’s values after many iterations? Are the
function’s values getting close to a particular number in each case?
6. Use the function gx x () 2 =− + with initial values of 4, 2, and 1. What happens
after many iterations with all three initial values? How do the results of all
three iterations relate to each other?