Teaching Algebra with Manipulatives

NAME ______________________________________________ DATE ____________ PERIOD ____
Algebra Activity
(Use with Algebra 2, Lesson 7-7)
Exploring Iteration
Each result of the iteration process is called an iterate.To interate a
function f(x), begin with a starting value x 0
, find f(x 0
), and call the result
x 1
. Then find f(x 1
), and call the result x 2
.Find f(x 2
) and call the result x 3
,
and so on.
Activity 1 Find the first three iterates, x 1
, x 2
, and x 3
, of the
function f(x) 1 2 x 5 for an initial value of x 0 2.
Step 1
Step 2
To obtain the first iterate, find the value of the function for
x 0
2.
f(x 0
) f(2)
1 (2) 5 or 6
2
To obtain the second iterate x 2
, substitute the function value
for the first iterate, x 1
, for x.
f(x 1
) f(6)
1 (6) 5 or 8
2
Step 3 Now find the third iterate, x 3
, by substituting x 2
for x.
f(x 2
) f(8)
1 (8) 5 or 9
2
Therefore, the first three iterates for the function f(x)
1 2 x 5 for an initial value of x 0
2 are 6, 8, and 9.
Model
Find the first three iterates of each function using the given
initial value. If necessary, round your answers to the nearest
hundredth.
1. g(x) 5x; x 0
0.2 2. g(x) 2x 1; x 0
0.5
Algebra 2—Chapter 7
3. g(x) 3 0.4x; x 0
4 4. g(x) 3x 0.5x 2 ; x 0
1
© Glencoe/McGraw-Hill 253 Teaching Algebra with Manipulatives