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?
5. Let's consider the linear function f(x) = -0.5x + 2.
If we choose initial values of x = 3 and x = 5, after many iterations, the function's values will approach the y-intercept of 2. In this case, the function's values are getting close to a particular number, which is the y-intercept.
6. For the function g(x) = 2 - x^2, when we use initial values of x = 4, x = 2, and x = 1, after many iterations, all three initial values will approach the y-intercept of 2. However, the rate at which they approach this value may vary due to the initial values being different. The results of all three iterations will ultimately converge to the same value, which is the y-intercept of 2.