Question

Find the first four iterates of the function f(x) = x2 with an initial value of x0 = -1.

a.
1, 1, 1, 1
c.
-1, -1, -1, -1
b.
1, -1, 1, -1
d.
-1, 1, -1, 1


Please select the best answer from the choices provided

Answer 1

A. 1, 1, 1, 1

Explanation:

We start with x0 = 1

x0 = -1 => f(x) = x² = (-1)² = 1

x1 = 1 => f(x) = x² = (1)² = 1

x2 = 1 => f(x) = x² = (1)² = 1

x3 = 1 => f(x) = x² = (1)² = 1

x4 = 1 => f(x) = x² = (1)² = 1

Answer 2

a. 1, 1, 1, 1

Explanation:

We'll use the formula f(x) = x² for each iteration. The output of the first iteration will be come the input of the second iteration, and so on.

We start with x0 = 1

x0 = -1 => f(x) = x² = (-1)² = 1

x1 = 1 => f(x) = x² = (1)² = 1

x2 = 1 => f(x) = x² = (1)² = 1

x3 = 1 => f(x) = x² = (1)² = 1

x4 = 1 => f(x) = x² = (1)² = 1