Use the initial value as the input of a function rule. This will give us the first output value.
-3, -18, -963
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&=2
f(x)& = -3x^2+9
To do so, we will use a table.
n
x_n
f(x)=-3x^2+9
x_(n+1)
0
x_0= 2
-3 x_0^2+9=-3( 2)^2+9
-3
1
x_1= -3
-3 x_1^2+9=-3( -3)^2+9
-18
2
x_2= -18
-3 x_2^2+9=-3( -18)^2+9
-963
3
x_3= -963
-
-
Therefore, the first three iterates of the function are -3, -18 and -963.
