△ABC has vertices at A(5,2), B(−3,1), and C(−2,5). Point D is located on the intersection of the altitude and AB¯¯¯¯¯¯¯¯, in such a way that D has coordinates at approximately (−1.5,1.2). Approximately how many units is the perimeter of △ABC?

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what graph

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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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