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McGraw Hill Glencoe Algebra 2, 2012

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McGraw Hill Glencoe Algebra 2, 2012 View details

5. Recursion and Iteration

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Exercise 41 Page 695

Use the initial value as the input of a function rule. This will give us the first output value.

4.25, 29.5625, 936.0664

Practice makes perfect

We are asked to write the first three iterates of a function, given a function rule and an initial value.

x_0&= 12 f(x)& = x^2+2x+3 To do so, we will use a table.

n	x_n	f(x)=x^2+2x+3	x_(n+1)
0	x_0= 1/2	x_0^2+2 x_0+3=( 1/2)^2+2( 1/2)+3	4.25
1	x_1= 4.25	x_1^2+2 x_1+3=( 4.25)^2+2( 4.25)+3	29.5625
2	x_2= 29.5625	x_2^2+2 x_2+3=( 29.5625)^2+2( 29.5625)+3	≈ 936.0664
3	x_3≈ 936.0664	-	-

Therefore, the first three iterates of the function are 4.25, 29.5625 and 936.0664.

Subchapter links

Check Your Understanding p.695

Practice and Problem Solving p.695-696

H.O.T. Problems p.696

Standardized Test Practice p.697

Spiral Review p.697

Skills Review p.697