Question

8．已知函數(shù)f（x）=$\left\{\begin{array}{l}{{x}^{2}-x，x＜0}\\{{e}^{x}，x≥0}\end{array}\right.$，則函數(shù)g（x）=f（x）-x-3的零點(diǎn)有2 個(gè)．

Answer 1

分析 函數(shù)g（x）=f（x）-x-3的零點(diǎn)個(gè)數(shù)即函數(shù)f（x）=$\left\{\begin{array}{l}{{x}^{2}-x，x＜0}\\{{e}^{x}，x≥0}\end{array}\right.$的圖象與函數(shù)y=x+3的圖象的交點(diǎn)個(gè)數(shù)，數(shù)形結(jié)合，可得答案．

解答 解：函數(shù)f（x）=$\left\{\begin{array}{l}{{x}^{2}-x，x＜0}\\{{e}^{x}，x≥0}\end{array}\right.$的圖象如下圖所示：

由圖可得函數(shù)f（x）的圖象與函數(shù)y=x+3的圖象有2個(gè)交點(diǎn)，
故函數(shù)g（x）=f（x）-x-3有兩個(gè)零點(diǎn)
故答案為：2．

點(diǎn)評(píng) 本題考查的知識(shí)點(diǎn)是函數(shù)的零點(diǎn)，分段函數(shù)的應(yīng)用，函數(shù)的圖象，難度中檔．