反比例函数具有下述十分浅显而又很有用的性质:①对于双曲线y=k/x(k≠0)上任一点P(x,y),恒有x·y=k(k为定值);②若点P(x,y)在双曲线y=k/x(k≠0)上,过P点作PA⊥x轴于点A,作PB⊥y轴于点B,O为坐标原点,则PA=BO=|y|,PB=OA=|x|。故S△OPA=S△OPB=1/2|x|·|y|=1/2|k|;③S距形OAPB=|x|·|y|=|k|。下面举例说明它们在解题中的应用。 The inverse function has the following very simple but very useful properties: ① For any point P (x, y) on the hyperbolic y = k / x (k ≠ 0), x · y = k (k is constant) ; ② if point P (x, y) is on hyperbolic y = k / x (k ≠ 0), then point P is taken as PA ⊥ x axis at point A, and PB ⊥ y axis is at point B, O is the coordinate origin , PA = BO = | y |, PB = OA = | x |. So S △ OPA = S △ OPB = 1/2 | x | · | y | = 1/2 | k |; S shape OAPB = | x | · | y | = | k |. The following examples illustrate their application in solving problems.