[CLA notes : Pay close attentions to the domains for each equations. ]

[CLA notes : A straight forward min-max problem where you have to be careful of the absolute value in the function. ]

[CLA notes : The key information to process is what it means for a function to have negative value for certain x value and positive value for different x value. In other word, remember the Intermediate Value Property of a function. ]

[CLA note : Just keep narrowing down the possibilities. Every clue here is important, and the whole thing is easier than it appears. ]

[CLA notes : Pay close attentions to the hatch marks on the graph.]

[CLA notes 2 : It is possible to guess the answers but the usual practice of the day was for the students to submit the work needed to arrive at the answer as well as the answers. Try to formally write out all the steps needed to arrive definitively at the answer.]

[CLA notes : Every bit of information reveals something important about the two circles. Be careful and be thorough in examination of the problem and expect the work involved to be made up of
multiple parts. ]

[CLA notes : Another straight forward problem. If you consider the properties involved, you can
easily note that there is a simple way to solve this problem. ]

[CLA note : A relatively straight forward problem that can be solved in multiple ways. It would be
good to practice all the different ways.]

      [CLA note : If you remember the distance formula and the Pythagorean Theorem , this problem is
        solvable. Remember to give as much details to the shape of the path of the point P ]