当绝对值x
人气:363 ℃ 时间:2020-04-03 10:40:55
解答
答:
|x|<=2,-2<=x<=2
y=x|x|-2x+1
1)当-2<=x<=0时:y=-x²-2x+1=-(x+1)²+2
对称轴x=-1,抛物线开口向下
所以:在[-2,0]上取得最大值为y(-1)=2
y(-2)=y(0)=1
所以:值域为[1,2]
2)当0<=x<=2时:y=x²-2x+1=(x-1)²
对称轴x=1,抛物线开口向上
所以:在[0,2]上取得最小值y(1)=0
y(0)=y(2)=1
所以:值域为[0,1]
综上所述,y的取值范围是[0,2]
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