senior high maths [Ch1.] transformations ⅢFunctions 北美高中数学第一章 转换 函数

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

The next concern is to find out what kind of relations are functions. First, a function is defined as follows:"For every value of the domain(x-value) there is one and only one value for the range(y-value)." What does this mean? It says any x-value can only have one y value. For example:
下一項重要的事是找出函數是怎樣的關係。首先，函數可以定義為：“對於定義域內每一個ｘ值，有且只有值域內的一個ｙ值與其相對應。” 這是什麼意思呢？它是說每個ｘ值只能有一個ｙ值。如以下例子：

a) (1,3), (2,4), (3,-1) is a function because each x-value 1, 2, 3 has only one value for y.  
　　(1,3), (2,4), (3,-1)是函數因為每個ｘ值１，２，３只有一個ｙ值。
b) (1,3), (-1,3), (2,4)is a function.
 　　 (1,3), (-1,3), (2,4)是函數。
c) (1,3), (1,2), (4,5) is not a function because x=1 gives y=2 and y=3, i.e., two values.
　　(1,3), (1,2), (4,5)不是函數因為ｘ＝１時，ｙ＝２並且ｙ＝３，有兩個值。

If "y" is an even power, then it can't be a function, e.g.,

X²+y²=9, y=±√(9-x²), (two values of y for each x value). If you can graph the equation, then remember the vertical line test: any vertical line can only cross the graph once if it is a function.
如果ｙ是偶次方的話，那麼他不可能成為函數，例如X²+y²=9, y=±√(9-x²)（有兩個ｙ值對應每個ｘ值）。如果你可以畫出函數圖像的話，記得垂直線測試：如果他是函數，任何一條垂直線只能與其圖形有一個交點。

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