Find the first four iterates of the function f(x) = 3x - 7 with an initial value of x0 = 4.
a.
-5, -8, -17, -44
c.
5, 8, 17, 44
b.
-7, -11, -15, -49
d.
7, 11, 15, 49

The answer is:

c. 5, 8, 17, 44

To find the iterates we need to take an initial input (x value) into the fuction, giving as result an output(iterate), then, the next input will be the previous output (iterate).

So,

Being w,x and y real numbers, the iterates are x, y, and z.

We are given the function,

Where, the initial input (x0) is 4

Now

- Iterating, starting with "x" equal to 4, we have:

So, the first iterate is 5.

- Iterating with "x" equal to 5, we have:

So, the second iterate is 8.

- Iterating with "x" equal to 8, we have:

So, the third iterate is 17.

- Iterating with "x" equal to 17, we have:

So, the fourth iterate is 44.

Hence, the iterates of the function with an initial value of x(0)=4 , are:

5, 8, 17, 44

Therefore, the correct option is c. 5, 8, 17, 44

Have a nice day!

one that is bigger than 3 1/2