I really need help on my last question if anyone can help me. 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?
what do you mean by "initial values?" Just values for x? If so, then
since g(x) = -x+2,plug in the value for every x:
g(4) = -2(4)+2 = -8+1 = -7
and do the same for any other desired values.
I still don't get what you mean by behavior after "iterations." What's going on here?
The equation describes a straight line. Other than that, I dunno what to say.
@Steve I think what they mean by behavior is if I see a pattern or trend with the iterations I was confused about that as well. Thank you for the example it made understanding it easier.
To determine what happens after many iterations with the initial values of 4, 2, and 1 using the function g(X)=-X+2, we can perform successive iterations and observe the results.
Let's start by performing iterations for each initial value:
1. For an initial value of 4:
- Iteration 1: g(4) = -(4) + 2 = -2
- Iteration 2: g(-2) = -(-2) + 2 = 4
- Iteration 3: g(4) = -(4) + 2 = -2
- Iteration 4: g(-2) = -(-2) + 2 = 4
- And so on...
2. For an initial value of 2:
- Iteration 1: g(2) = -(2) + 2 = 0
- Iteration 2: g(0) = -(0) + 2 = 2
- Iteration 3: g(2) = -(2) + 2 = 0
- Iteration 4: g(0) = -(0) + 2 = 2
- And so on...
3. For an initial value of 1:
- Iteration 1: g(1) = -(1) + 2 = 1
- Iteration 2: g(1) = -(1) + 2 = 1
- Iteration 3: g(1) = -(1) + 2 = 1
- Iteration 4: g(1) = -(1) + 2 = 1
- And so on...
Now, let's analyze the results for each initial value:
1. For the initial value of 4:
- After many iterations, the value oscillates between -2 and 4. It doesn't converge to a specific value but keeps alternating between these two values.
2. For the initial value of 2:
- After many iterations, the value oscillates between 0 and 2. Similar to the previous case, it doesn't converge to a specific value but alternates between these two values.
3. For the initial value of 1:
- Interestingly, after every iteration, the value remains constant at 1. It does not change or converge to any other value but stays fixed.
Therefore, the results of all three iterations involve oscillation or a fixed value:
- For the initial values of 4 and 2, the values oscillate between two specific values (either -2 and 4 or 0 and 2).
- For the initial value of 1, the value remains fixed at 1 with no change.
In summary, the results of all three iterations are different, with the initial values of 4 and 2 showing oscillating behavior while the initial value of 1 remains constant.