Consider the following game. there is a bottle with 20 colored chips inside. there are 2 blue chips, 4 purple chips, 7 green chips, and 7 red chips. you pay $2 and pick one out at random. if you pick a blue chip, you get a prize of $10. if you pick a purple chip, you get a prize of $5. you get nothing for red or green chips. what is the expected value of playing the game? $2 $0 –$2 –$0.50

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guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

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