A12-inch candle is lit and steadily burns until it is burned out. as the burned length of the candle increases from 4 to 7.5 inches, the remaining length of the candle varies from inches to inches. suppose b represents the burned length of the candle in inches (or the number of inches that have burned from the candle since it was lit). write an expression in terms of b that represents the remaining length of the candle (in inches).

m a t h w a y. c o m

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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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6 cm

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