5. Recursion and Iteration
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Use the initial value as the input of a function rule. This will give us the first output value.
-18, 74, -294
We are asked to write the first three iterates of a function, given a function rule and an initial value.
| n | x_n | f(x)=-4x+2 | x_(n+1) |
|---|---|---|---|
| 0 | x_0= 5 | -4 x_0+2=-4( 5)+2 | -18 |
| 1 | x_1= -18 | -4 x_1+2=-4( -18)+2 | 74 |
| 2 | x_2= 74 | -4 x_2+2=-4( 74)+2 | -294 |
| 3 | x_3= -294 | - | - |
Therefore, the first three iterates of the functions are -18, 74 and -294.