Start with the basic function f(x)=2x. If you have an initial value of 1, then you end up with the following iterations. f(1)=2*
1=2 f^2(1)=2*2*1=4 f^3(1)=2*2*2*1=8 1. If you continue this pattern, what do you expect would happen to the numbers as the number of iterations grows? Check your result by conducting at least 10 iterations. 2. Repeat the process with an initial value of −1. What happens as the number of iterations grows?
1. If you
continue this pattern, what do you expect would happen to the numbers as
the number of iterations grows?
I expect the numbers continue growing multiplying each time by 2.
Check your result by conducting at
least 10 iterations.
f^4(1) = f^3(1) * f(1) = 8*2 = 16
f^(5)(1) = f^4(1) * f(1) = 16 * 2 = 32
f^6 (1) = f^5 (1) * f(1) = 32 * 2 = 64
f^7 (1) = f^6 (1) * f(1) = 64 * 2 = 128
f^8 (1) = f^7 (1) * f(1) = 128 * 2 = 256
f^9 (1) = f^8 (1) * f(1) = 256 * 2 = 512
f^10 (1) = f^9 (1) * f(1) = 512 * 2 = 1024
2. Repeat the process with an initial value of −1.
What happens as the number of iterations grows?
f(-1) = 2(-1) = - 2
f^2 (-1) = f(-1) * f(-1) = - 2 * - 2 = 4
f^3 (-1) = f^2 (-1) * f(-1) = 4 * (-2) = - 8
f^4 (-1) = f^3 (-1) * f(-1) = - 8 * (-2) = 16
f^5 (-1) = f^4 (-1) * f(-1) = 16 * (-2) = - 32
As you see the magnitude of the number increases, being multiplied by 2 each time, and the sign is aleternated, negative positive negative positive ... </span>
When you multiply fractions you want to make them a mixed number then multiply the two top numbers together and then the bottom two together. Basically 6 2/3 would become 20/3 x 5/6... then multiply 5 and 20 together and 3 and 6 together to get 100/18... simplify from there.
