Consider the tent map defined by T (x) =



2x, 0 ≤ x < 1 2 , 2(1 − x), 1 2 ≤ x ≤ 1.

Sketch graphical iterations for the initial conditions (i) x0 = 1 4 , (ii) x0 = 1 6 ,

(iii) x0 = 5 7 , and (iv) x0 = 1 19 . Find the points of periods one, two, three, and four. Give a formula for the number of points of period N.