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.
-21, -123, -735
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)=6x+3 | x_(n+1) |
|---|---|---|---|
| 0 | x_0= -4 | 6 x_0+3=6( -4)+3 | -21 |
| 1 | x_1= -21 | 6 x_1+3=6( -21)+3 | -123 |
| 2 | x_2= -123 | 6 x_2+3=6( -123)+3 | -735 |
| 3 | x_3= -735 | - | - |
Therefore, the first three iterates of the functions are -21, -123 and -735.