High School

Find the first three iterates of the function [tex]f(x) = x^2 + 4[/tex] with an initial value of [tex]x_0 = -3[/tex]. If necessary, round your answers to the nearest hundredth.

1) 13; 175; 20,933
2) 13; 173; 19,933
3) 13; 173; 29,967
4) 13; 173; 29,933

Answer :

Final answer:

The first three iterates of the function f(x) = x² + 4, starting from Xo = -3, are 13, 173, and 29,933.

Explanation:

The first three iterates of the function f(x) = x² + 4 with an initial value of Xo = -3 can be found by repeatedly applying the function to the previous result. Let's calculate each iterate step by step:

  1. f(Xo) = f(-3) = (-3)² + 4 = 9 + 4 = 13

  2. f(f(Xo)) = f(13) = 13² + 4 = 169 + 4 = 173

  3. f(f(f(Xo))) = f(173) = 173² + 4 = 29929 + 4 = 29933

Therefore, the first three iterates of the function are 13, 173, and 29,933.

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