分段函数为初等函数的判定定理

Piecewise Function——Judgement Theorem of Elementary Funtion

函数为初等函数的必要条件是函数在定义域内为连续函数。定义在区间I上的由有限个初等函数表示的分段函数仍为初等函数的充分条件为函数在I上连续 ,此时分段函数可由一个符合初等函数定义的式子表示。

The necessary condition of a function being an elementary function is that the function is a continuous function in the field of definition.That the function continues in I is the sufficient condition of a piecewise function being elementary function was expressed by a finite number of elementary functions defined in the interval I.At such a time,the piecewise function can be expressed by an expression that accords with the definition of elementary function.[KH2D]