什麽是函数函数像一个魔术师的戏法箱,适当输入就一.ppt

什麼是函數？ 函數像一個魔術師的戲法箱，適當“輸入”就一定會有“輸出”，而且相同的輸入必定會得到相同的輸出。 Ex:輸入的值是車子行駛的時間，輸出的 值是車子行駛的距離 得到一個函數描述該車的行駛狀況 Why do we need domains and ranges?  Domains and ranges are important ideas that will help us to understand the relationship between two variables in an equation, especially when we begin graphing. 如果行車速度固定為每小時 v0 公里， 距離函數則為 公里 （t 以分鐘為單位），函數圖形都會是一條直線。而且這條直線的斜率為 這裡的運動為等速度，所以每一瞬間的速度也等於平均速度。 當函數圖形無法以一條直線來表示，對於這樣的函數，能發現它每一刻的“瞬間速度”嗎？ What is a function? In general, a compact description of the data, that gives the values of some of the fields in terms of the others, is called a function. A variable y is a function of x if a relation between x and y produces exactly one value of y for each value of x.  The variable x is called the independent variable. If y = f(x) we call y the dependent variable. A function can be specified: numerically: by means of a table algebraically: by means of a formula graphically: by means of a graph A Numerically Specified Function:  Ex: Suppose that the function f is specified by the following table. An Algebraically Specified Function: Ex: Suppose that the function f is specified by f(x) = 3x2 - 4x + 1. Then f(2)= 3(2)2 - 4(2) + 1? Substitute 2 for x= 12 - 8 + 1 = 5? f(-1)= 3(-1)2 - 4(-1) + 1? Substitute -1 for x= 3 + 4 + 1 = 8?  In other words, a function maps one type of value to another. The set X is the domain and the set y is the range of the function. How do we find Domains Ranges Suppose that we let X be 0, then If we let X be -3, -2, -1, 0, 1, 2, 3 respectively and substitute each value of X into the equation, then the set of ordered pairs would be: If we use the set of ordered pairs above to plot the graph, the graph would be: The domain for the above function is the set of all real numbers. If we examine the set of ordered pairs, it will include {..., -3, -2, -1, 0, 1, 2, 3, ...}. The rang