The Map

As you walk through Gate 4, you realize that Gate 5is nowhere to be found. In front of you lies an expansive desert as far as you can see. You look at your map and see that there is analert for this area. The warning states that this desert is almost entirely quicksand, with only one path safely through the desert. That path is defined by a piecewise function but requires that some parameters be determined before your computer can generate the plot. Thinking back on what you learned in calculus, you realize that your path will need to be continuous. You just need to tell your computer what the parameters below should be in order to create this continuous path. What parameters do you give your computer?

f(x)=8,x+A,Bx+3,2x+C,Dx1,3,x222()={8,2+,2<1+3,1<02+,0<11,1<23,>2

A	B	C	D

Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team.