y軸反射

1、(a) 把y = f(x)的圖像向上平移k單位。,,y = f(x),y = f(x)+k,k單位,平移,即圖像上的每點的y坐標,加上k。,所得圖像所表示的函數(shù)為,y = f(x),+k,,上加,,(b) 把y = f(x)的圖像向下平移k單位。,,,y = f(x),y = f(x)－k,k單位,平移,即圖像上的每點的y坐標,減去k。,所得圖像所表示的函數(shù)為,y = f(x),－k,,下減,y = f(x ),(c) 把y =

2、 f(x)的圖像向左平移h單位。,平移,y1 = y2,，x1 = x2+h,所得圖像所表示的函數(shù)為,y = f(x),+h,,左加,y = f(x),,,(x1 , y1),(x2 , y2),∵ y1 = f(x1),∴ y2 = f(x2 +h),y = f(x+h),k單位,(d) 把y = f(x)的圖像向右平移h單位。,平移,y1 = y2,，x1 = x2－h(huán),所得圖像所表示的函數(shù)為,y = f(x),,右減,y = f(

3、x),,,(x1 , y1),(x2 , y2),∵ y1 = f(x1),∴ y2 = f(x2 －h(huán)),y = f(x ),－h(huán),y = f(x－h(huán)),k單位,(a) 把y = f(x)的圖像沿x軸反射。,y = f(x),y = －f(x),,,反射,即圖像上的每點的y坐標,正負號顛倒。,所得圖像所表示的函數(shù)為,y = f(x),－,y = f(x),,,,(b) 把y = f(x)的圖像沿y軸反射。,y =

4、f(x),y = f(－x),,反射,即圖像上的每點的x坐標,正負號顛倒。,所得圖像所表示的函數(shù)為,y = f(x),－,y = f( x),,,,伸縮,(a) 把y = f(x)的圖像垂直伸縮。,(i) 垂直伸展至原來的k1倍，其中k1＞1。,y = f(x),y = f(x),,即圖像上的每點的y坐標,乘以k1。,所得圖像所表示的函數(shù)為,k1,y = f(x),y = k1f(x)，k1＞1,伸縮,(a) 把y = f

5、(x)的圖像垂直伸縮。,(ii) 垂直收縮至原來的k2，其中0＜k2＜1。,y = f(x),y = f(x),,即圖像上的每點的y坐標,乘以k2。,所得圖像所表示的函數(shù)為,y = f(x),k2,y = k2f(x)，0＜k2＜1,,伸縮,(b) 把y = f(x)的圖像水平伸縮。,,,y = f(k1x)，k1＞1,y = f(x),(x1 , y1),(x2 , y2),y1 = y2,，x1 = k1x2,∵ y1

6、= f(x1),∴ y2 = f(k1x2),所得圖像所表示,k1,y = f( x),y = f(x),的函數(shù)為,伸縮,(b) 把y = f(x)的圖像水平伸縮。,,,y = f(k2x)，0＜k2＜1,y = f(x),(x1 , y1),(x2 , y2),y1 = y2,，x1 = k2x2,∵ y1 = f(x1),∴ y2 = f(k2x2),y = f( x),k2,y = f(x),所得圖像所表示,的函數(shù)為