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

g(x)= -2|x-2|+4

I tried to do this but it isn't looping so I think I'm doing it wrong. Help!

It "loops" again at iteration ^13; where you get 2.24, likewise at iteration ^3. And again at iteration ^14, where you get 3.52, likewise at ^4. I am unsure if this is the definition of the "loop". My book doesn't explain if a loop is where you keep getting the same number after a certain iteration, or you will "loop" back around the iteration and then keep going? Can you please tell me if I'm right? Thank you in advance.

Not sure what you want. Do you mean that g is replaced by the previous value of g, so that

g(n+1) = -2|g(n)-2|+4

??
Otherwise, how do you get any looping activity?

4 years and one day later, my best answer is to do loop-de-loops on a rollercoaster. math sucks

To determine the loop that forms for the given function, we need to understand the behavior of the function over multiple iterations. In this case, the function is described as:

g(x) = -2|x-2| + 4

To find the loop, we start by choosing a value for x and plugging it into the function. Let's start with an initial value of x = 1.72:

g(1.72) = -2|1.72-2| + 4
= -2|-0.28| + 4
= -2(0.28) + 4
= -0.56 + 4
= 3.44

The result is 3.44. Now, we take this value and plug it back into the function to get the next value:

g(3.44) = -2|3.44-2| + 4
= -2|1.44| + 4
= -2(1.44) + 4
= -2.88 + 4
= 1.12

Continuing this process, we keep plugging the result of each iteration back into the function to get the next value. Let's go through a few more iterations:

g(1.12) = -2|1.12-2| + 4
= -2|-0.88| + 4
= -2(0.88) + 4
= -1.76 + 4
= 2.24

g(2.24) = -2|2.24-2| + 4
= -2|0.24| + 4
= -2(0.24) + 4
= -0.48 + 4
= 3.52

g(3.52) = -2|3.52-2| + 4
= -2|1.52| + 4
= -2(1.52) + 4
= -3.04 + 4
= 0.96

As you can see, the values seem to be oscillating between 1.12, 2.24, 3.52, and 0.96. This indicates the presence of a loop or cycle.

If your calculations aren't showing this looping behavior, it's possible that you made an error during the calculations. Make sure to double-check each step for accuracy.