The function f (x) = - 1/4 (x) + 1 is getting closer to a particular number. Its initial values are 4 and - 2, what happens to the values of the function's after 10 iterations. What number are the function's values getting closer to each time?

After 10 iterations, the value is approximately the value it gets closer each time, which is 0.8 (or 4/5)

Step-by-step explanation:

If the inicial value is 4, we have:

1: f (4) = - 1/4 (4) + 1 = 0

2: f (0) = - 1/4 (0) + 1 = 1

3: f (1) = - 1/4 (1) + 1 = 3/4

4: f (3/4) = - 1/4 (3/4) + 1 = 13/16

5: f (13/16) = - 1/4 (13/16) + 1 = 51/64

6: f (51/64) = - 1/4 (51/64) + 1 = 205/256

7: f (205/256) = - 1/4 (205/256) + 1 = 819/1024

8: f (819/1024) = - 1/4 (819/1024) + 1 = 3277/4096

9: f (3277/4096) = - 1/4 (4) + 1 = 13107/16384

10: f (13107/16384) = - 1/4 (13107/16384) + 1 = 52429/65536 = 0.8

If the inicial value is - 2, we have:

1: f (-2) = - 1/4 (-2) + 1 = 3/2

2: f (3/2) = - 1/4 (3/2) + 1 = 5/8

3: f (5/8) = - 1/4 (5/8) + 1 = 27/32

4: f (27/32) = - 1/4 (27/32) + 1 = 101/128

5: f (101/128) = - 1/4 (101/128) + 1 = 411/512

6: f (411/512) = - 1/4 (411/512) + 1 = 1637/2048

7: f (1637/2048) = - 1/4 (1637/2048) + 1 = 6555/8192

8: f (6555/8192) = - 1/4 (6555/8192) + 1 = 26213/32768

9: f (26213/32768) = - 1/4 (26213/32768) + 1 = 104859/131072

10: f (104859/131072) = - 1/4 (104859/131072) + 1 = 419429/524288 = 0.8