Example 3 Nonlinear functions can lead to some interesting results. Using the function g(x)= -2|x-2|+4 and the initial value of 1.5 leads to the following result after many iterations. • g(1.5)=...

Example 3

Nonlinear functions can lead to some interesting results. Using the function
g(x)= -2|x-2|+4  and the initial value of 1.5 leads to the following result after many iterations.

• g(1.5)= -2|1.5-2|+4=2

• g^2 (1.5)=g(3)=2|3-2|+4=2

• g^3 (1.5)=g(2)=-2|2-2|+4=4

• g^4 (1.5) =g(4)=-2|4-2|+4=0

•g^5 (1.5) =g(0)=-2|0-2|+4=0

At this point, further iterations of the function will repeatedly obtain zero. You can conclude that repeated iterations of the function with an initial value of 1.5 will lead to a value of zero. For most values of this function, repeated iterations will lead to looping values. The next set of questions will address this concept.

A) What is the loop that forms after many iterations when the initial value of g is 1.7?

B) What is the loop that forms after many iterations when the initial value of g is 1.72?