中四maths thansformation of graphs of functions 唔明,可唔可以入黎教我?

首先你睇左以下的一些做法

y = -f(x)的意思是將y = f(x)在x-axis上下反轉

y = f(-x)的意思是將y = f(x)在y-axis左右反轉

y = a + f(x)的意思是將y = f(x)上升了a格

y = -a + f(x) 的意思是將y = f(x)下降了a格

y = af(x)的意思是將y = f(x)變高了a倍

y = (1/a)f(x) 的意思是將y = f(x)變矮了a倍

y = f(ax)的意思是將y = f(x)變廋了a倍

y = f(x/a)的意思是將y = f(x)變肥了a倍

y = f(x+a) 的意思是將y = f(x)向左行了a格

y = f(x-a) 的意思是將y = f(x)向右行了a格

所以答案如下：
1.Translate 10 units downwards and 2 units to the left
向下10格及向左2格
y = f(x+2) - 10
所以是 y = (x+2)^2 - 10

2.Translate 3 units downwards and then reflect along the y-axis
向下3格後y-axis左右反轉
y = f(-x) - 3
所以是 y = (-x)^2 - 3

3.Translate 3 units downwards and then reflect along the x-axis
向下3格後x-axis上下反轉
y = -[f(x) - 3]
所以是 y = -[(x)^2 - 3]

4.Reflect along the y-axis and then translate 3 units downwards
y-axis左右反轉後向下3格後
y = f(-x) - 3
所以是 y = (-x)^2 - 3

5. Reflect along the y-axis and then translate 4 units to the left.
y-axis左右反轉後和左4格
y = f(-x + 4)
所以是 y = (-x+4)^2

希望以上幫到你明白transformation

2008-02-25 00:55:34 補充：
回答者gsoper123答的第5題錯了因為Reflect along the y-axis and then translate 4 units to the left是先y-axis左右反轉後和左4格所以是首先y = f(-x)然後先係y = f(-x + 4)所以答案是y = (-x+4)^2而唔係y = (x + 4)^2

y = m (x - k) + c

m係slope : +ve會係向左斜 ( / )
-ve會同向右斜 ( \ ) 即係 +ve ge slope reflect along x-axis
所以m用黎做reflection along x-axis

k就係左右移動 :
+ve ge話，(x - k) 就會向右移 k units
-ve ge話，(x - k)就會變左(x + k)，即係向左移 k units
可以好似做 (x - 1)(x + 2) = 0 咁
x 會 = 1 or -2
(x - k)會k其實就係個cruve/line
passes through/touches 果點ge x co-ordinate

c就係 y-intercept :
+ve ge話成個graph就會向上移c units
-ve ge話成個graph就會向下移c units


1. y = (x + 2)^2 - 10
[ x coordinate由 0 去左 -2, y-int由0去左-10]

2. y = (- x)^2 - 3
→ y = x^2 + 3
[ (-x) 就係將 x ge coordinate 左右調轉, 即係reflect along y-axis ]

3. y = - ( x^2 - 3)
→ y = - x^2 + 3

4. y = (- x)^2 - 3
→ y = x^2 - 3

5. y = [ - (x + 4) ]^2
→ y = (x + 4)^2

如果唔明的話
可以用畫graph ge方式黎做
仔細咁諗下數字同graph ge關係
自自然然做transformation ge時候
腦裏面會出到graph