Chaos theory portfolio algebra 2 answers

I don’t know how to handle this Algebra question and need guidance.

Need 12 questions answered as described on attached portfolioChaos Theory Portfolio Directions: In this portfolio, you will use repeated function composition to explore elementary ideas that are used in the mathematical field of chaos theory. Items under the Questions headings will be submitted to your teacher as part of your portfolio assessment. For all questions, make sure to be complete in your responses. This can include details such as the function being iterated, the initial values used, and the number of iterations. The phrase many iterations is used in some of the questions. Interpret that to mean using enough iterations so that you can come to a conclusion. If necessary, round decimals to the nearest ten-thousandth. Questions 1. If you continue this pattern, what do you expect would happen to the numbers as the number of iterations grows? Check your result by conducting at least 10 iterations. 2. Repeat the process with an initial value of -1. What happens as the number of iterations grows? Example 2 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 < m < 0. 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 g(x) = -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? Questions 7. What is the loop that forms after many iterations when the initial value of g is 1.7? 8. What is the loop that forms after many iterations when the initial value of g is 1.72? Questions 9. Choose an initial value that is between zero and 4 and is not a whole number. Iterate it using the function, f, ten times. If necessary, you can round your results to the nearest ten-thousandth. 10.Choose a second initial value that is 0.01 greater than the initial value from question 9. Iterate it using the function, f, ten times. If necessary, you can round your results to the nearest ten-thousandth. 11.Is there a relationship between the ten values from question 9 and the ten values in question 10? ...
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