Think of a function as a math machine with an input and an output. Suppose the function is A(x) = 3x + 1. That means if you put any number (x) into this function machine, the machine will multiply the number by three and add one. For example, what is the output if five is the input? Five times three plus one equals 16 for the output. That's written A(5) = 16. Suppose you join two function machines so that the output of the first one is connected to the input of the second one. Let's make the second function B(x) = x^2, (remember that x^2 means x squared). If you put two into the A machine, out comes seven. Then seven is the input to the B machine which squares it, and out comes 49. Okay? That's written B(A(2)) = 49.
Here are five functions:
A(x) = 4x - 3
B(x) = 3x^2
C(x) = 7x + 1
D(x) = x^2
E(x) = 2x + 7
I am going to connect them in alphabetical order and use two as the input number. That would be written as E(D(C(B(A(2))))). The resulting output = 553,359.
What arrangement of functions will produce the largest output with two as the input (each function used only once)? I am looking for logical reasoning and algebra rather than just guess and check. Explain why you chose your particular arrangement. (Just write the order of your functions for the short answer.)
When it came to solving this POW you should have noticed there were two types of equations present linear and exponential. Knowing that eponentials grow so rapidly you would want to use their power as the end of the string of equations and the linears up front. You would test the class of equations to see which would produce the highest yeild in its group and order accordingly.
How did you do?
