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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 40 Page 695

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

-2, 3, 6.75

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&=8 f(x)&=-0.25x^2+x+6 To do so, we will use a table.

n	x_n	f(x)=-0.25x^2+x+6	x_(n+1)
0	x_0= 8	-0.25 x_0^2+ x_0+6=-0.25( 8)^2+ 8+6	-2
1	x_1= -2	-0.25 x_1^2+ x_1+6=-0.25( -2)^2+( -2)+6	3
2	x_2= 3	-0.25 x_2^2+ x_2+6=-0.25( 3)^2+ 3+6	6.75
3	x_3= 6.75	-	-

Therefore, the first three iterates of the function are -2, 3 and 6.75.

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