Question

1. find the first 3 iterates of the function $f(x) = -2x + 3$ when $x_0 = 0$.

○ 3, -3, 9
○ 1, 1, 1
○ 2, -1, 5
○ -2, 0, 2

Explanation:

Step1: Calculate first iterate ($x_1$)

Substitute $x_0=0$ into $f(x)$:
$x_1 = f(x_0) = -2(0) + 3 = 3$

Step2: Calculate second iterate ($x_2$)

Substitute $x_1=3$ into $f(x)$:
$x_2 = f(x_1) = -2(3) + 3 = -3$

Step3: Calculate third iterate ($x_3$)

Substitute $x_2=-3$ into $f(x)$:
$x_3 = f(x_2) = -2(-3) + 3 = 9$

Answer:

3, -3, 9