函数中的任意性和存在性问题,一直是教与学的重点和难点,也是高考数学的热点、重点、难点。其中,双变量的任意性或存在性问题是函数、方程、不等式等内容交汇处的一个十分活跃的考点,学生在求解时极易混淆、出错,因此备受命题者的青睐。对此问题,笔者以结论的形式归纳整理,供同仁在教学中参考。 Arbitrary and existential problems in the function, has always been the focus and difficulty of teaching and learning, but also the entrance exam mathematics hot, important and difficult. Among them, the bivariate arbitrarily or existential problem is a very active test site for functions, equations, inequalities and other content interchanges. Students are very confused and error-prone when solving, so they are favored by the proponents. On this issue, the author summarized the form of conclusions for my colleagues in teaching reference.