Sunday, January 6, 2013

senior high maths [Ch1.] transformations Ⅳ Translation of Graphs (a) 北美高中数学第一章 转换 圖形的轉換(上)

 From Theory and problems for senior high math 
来自 Theory and problems for senior high math   

Translation of graphs圖形的轉換
The graph of the function y=f(x) consists of all points (x,y) whose co-ordinates satisfy the equation.
y=f(x) 這個函數圖像組合了所有滿足這個等式的點(x,y)。

a) Vertical shifts, a>0垂直平移
   For the graph of y=f(x), the graph of :對於函數圖像y=f(x)來說,以下圖像:
   
y=f(x)+a is shifted up 'a' units
 y=f(x)+a向上平移a個單位
y=f(x)-a  is shifted down 'a' units
 y=f(x)+a向下平移a個單位

Examples:例子
QUADRATIC GRAPHS: 二次函數

y=x2

y=x2+1

 
 
y=x2-2

 SQUARE ROOT GRAPHS:平方根函數
 y=√x

 y=√x -2

 y=√x+1

ABSOLUTE VALUE GRAPHS:絕對值函數
y=|x|

 
 y=|x| +1

 y=|x|-2

CUBIC GRAPHS:三次方函數

y=x3

y=x3+1

y=x3-2
 
RECIPROCAL GRAPHS:倒數函數
y=1/x

 
 y=1/x +1

  
y=1/x -2

 Translate by Annabelle Wu
翻譯自 Annabelle Wu