Find the first four iterates of the function f(x) = 2x with an initial value of x0 = 2.
a.
4, 6, 8 ,10
c.
2, 4, 8, 16
b.
2, 4, 6, 8
d.
4, 8, 16, 32

select the best answer from the choices provided

d.  4, 8, 16, 32

Step-by-step explanation:

We'll use the formula  f(x) = 2x  for each iteration.  The output of the first iteration will be come the input of the second iteration, and so on.

So, we start with x0 = 2 and we plug that into the base equation:

x0 = 2 ==> f(x) = 2(2) = 4

x1 = 4 ==> f(x) = 2(4) = 8

x2 = 8 ==> f(x) = 2(2) = 16

x3 = 16 ==> f(x) = 2(2) = 32

x4 = 32 ==> f(x) = 2(2) = 64

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.