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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 42 Page 695

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

1, 4, 37

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)& = 2x^2+x+1 To do so, we will use a table.

n	x_n	f(x)=2x^2+x+1	x_(n+1)
0	x_0= -1/2	2 x_0^2+ x_0+1=2( -1/2)^2+( -1/2)+1	1
1	x_1= 1	2 x_1^2+ x_1+1=2( 1)^2+ 1+1	4
2	x_2= 4	2 x_2^2+ x_2+1=2( 4)^2+ 4+1	37
3	x_3= 37	-	-

Therefore, the first three iterates of the function are 1, 4 and 37.

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