Question

4．函數(shù)y=$|\begin{array}{l}{{x}^{2}-3x+2}\end{array}|$-b，b∈（0，$\frac{1}{4}$）的零點個數(shù)是（　�。�

• A． 1個
• B． 3個
• C． 2個
• D． 4

Answer 1

分析 作函數(shù)y=$|\begin{array}{l}{{x}^{2}-3x+2}\end{array}|$的圖象，從而由圖象的交點可得函數(shù)的零點的個數(shù)．

解答 解：作函數(shù)y=$|\begin{array}{l}{{x}^{2}-3x+2}\end{array}|$的圖象如下，
，
故函數(shù)y=$|\begin{array}{l}{{x}^{2}-3x+2}\end{array}|$與函數(shù)y=b有四個交點，
故方程$|\begin{array}{l}{{x}^{2}-3x+2}\end{array}|$=b，b∈（0，$\frac{1}{4}$）有四個解，
故函數(shù)y=$|\begin{array}{l}{{x}^{2}-3x+2}\end{array}|$-b，b∈（0，$\frac{1}{4}$）的零點個數(shù)是4，
故選：D．

點評 本題考查了函數(shù)的圖象的應(yīng)用．