9
QuizMultiple Choice

Sequences and Iteration

Question 9 • TX-Advanced Quantitative Reasoning

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

Answer
A
1, 1, 1, 1
B
1, -1, 1, -1
C
-1, -1, -1, -1
D
-1, 1, -1, 1

Explanation

The function is f(x) = x². Starting with x₀ = −1, the first iterate is x₁ = (−1)² = 1; applying the function again keeps the value at 1. Thus x₁, x₂, x₃, and x₄ are 1, 1, 1, 1, matching choice A: 1, 1, 1, 1.

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