确定职能

播放段落

Drop-Down List s
::下下列表

播放段落

A n example of a function in computer programming is a drop-down list. A drop-down list is a function which takes in the user’s input choice and returns a predetermined output. The output can be in the form of a number or an action. The user’s input choice comes in the form of the position of the selection, which begins at position 0 for the first item on the list. If the user chooses the item in position 3, then the function will take that information and return an appropriate outcome as determined by the computer programmer.
::计算机编程中函数的示例是下拉列表。 下拉列表是用户输入选择中的函数, 并返回一个预设输出。 输出的形式可以是数字或动作。 用户输入选择的形式是选择位置, 从列表中第一个项目的位置 0 开始。 如果用户选择了位置 3 中的项目, 则该函数将使用该信息, 并返回计算机程序员确定的适当结果 。

播放段落

Explore the drop-down list below and determine the relationship between position and color.
::探索下面的下拉列表并确定位置和颜色之间的关系 。

播放段落

Discussion Question
::讨论问题

播放段落

Explain the relationship between the input position and the output color. What do you notice?
::解释输入位置和输出颜色之间的关系。 您注意到什么 ?

  

---

播放段落

Functions vs. Relations
::职能与关系

播放段落

As you saw in the previous interactive, it is possible in computer programming for one input to have multiple outputs. This relationship was accomplished in the interactive using an 'if' statement, which is a grammar-based conditional statement, and a randomly chosen value. However, in mathematics,  this is not considered a function. As you may have already learned in the lesson , a function is a special type of relation where every input has a single output. Every element of the domain must  have one and only one corresponding element  in the range . It is possible  in a function to have two different inputs  with the same output. Many of the examples of functions that  you have seen so far have repetitive outputs.
::正如您在上次互动中看到的那样,在计算机编程中,一个输入可以有多个输出。这种关系是在交互式语句“if”中实现的,这是一个基于语法的有条件语句,并且是一个随机选择的值。但是,在数学中,这不算是一个函数。正如您在教训中已经学到的,函数是一种特殊的关系,其中每个输入都有单一输出。域的每个元素都必须在范围中有一个和唯一的对应元素。在函数中,可以有两个不同的输入,并且输出相同。迄今为止你所看到的功能的许多例子都有重复输出。

播放段落

One way to think of the difference between a function and a relation that is not a function is to think of functions as being  trustworthy : If a relation is a function, you can always trust that  every unique input will always   return the same output every time. In the color interactive example above, you can't trust that you will always get the same output (color) every time you choose a specific input ( number - specifically 2 ), so the color/number relationship is  not a function.
::计算函数与非函数关系之间的差别的一种方式是将函数视为可信赖性:如果关系是一个函数,您可以总是相信每个独特的输入总是每次返回相同的输出。在上文的颜色互动示例中,您不能相信每次选择一个特定输入(数字 - 具体2)时总是得到相同的输出(颜色),因此颜色/数字关系不是一个函数。

播放段落

Example
::示例示例示例示例

播放段落

Are the relations below functions?
::以下关系是否具有职能?

播放段落
1. Ordered Pairs
   ::有序对等

{(-3, 4) (2, 9) (1, 5) (10, -12) (2, 3)}

播放段落
• Th is set of ordered pairs  is not a function because the input value 2 leads to output values of both 9 and 3. Look at this relation when displayed in different forms.
  ::这组有顺序的配对不是一个函数, 因为输入值 2 导致输出值为 9 和 3 。 当以不同形式显示时, 请查看此关系 。

播放段落
2. Table
   ::表格表表表表

播放段落

::输入输出 - 34291510-1223

播放段落
• In table format, you can see that t his set of points is not a function because the input value "2" leads to output values of both 9 and 3. 
  ::在表格格式中,您可以看到,这组点不是一个函数,因为输入值“2”导致输出值为9和3。

播放段落
3. Mapping Diagram
   ::绘图图图图

播放段落

You can tell that this relation is not a function because the input value 2 has arrows pointing to both 3 and 9.
::您可以告诉您此关系不是一个函数, 因为输入值 2 指向 3 和 9 的箭头。

播放段落

Discussion Question
::讨论问题

播放段落
1. Can a function have two arrows from different input values pointing to the same value? Give an example.
   ::函数能否有两个来自不同输入值的箭头指向相同值?请举一个例子。
播放段落
2. Graph the following functions on different graphs:
   1. {(3,6),(1,2),(0,3),(5,-2),(4,0)}
   2. {(-3,-1),(-1,5),(0,3),(2,3),(0,-4)}
   3. {(3,4),(-2,4),(-1,-1),(1,4),(5,5)}
   4. {(1,3),(3,1),(1,-5),(1,0),(-3,2)} 
   
   ::{(3)6,(1)2,(0)3,(5)2,(4,0)}{(3)3,(3)-1,(1)5,(0)3,(3)3,(3)3,(0)4,(0)4}{(3)4,(2)4,(1)-1,(1)4,(5)4,(5)}{(1,3)3,(1)1,(1)5,(1)5),(1)3,(1)5),(1,(1),(1,0),(3),(3)}}}(3,(3)4,(2)4,(1),(1,4),(4),(4),(5),(5)}{(1,3,(3),(1),(1,)5),(1,(1),(5),(1)5),(1,(1),(1),(1,)0,(3),(3),(3),(3))
播放段落
3. What similarities do you notice between graphs that form functions and graphs that do not form functions?
   ::显示函数的图形与不显示函数的图形之间有什么相似之处?

  

---

播放段落

Is it a Function?
::是"功能"吗?

播放段落

To determine whether a relation is a function, you need to check whether one input value leads to two different output values. If one  input value does lead to two different output values, you will be able to tell visually because the two points will  line up vertically .  You can  often find  this using what is called “The Vertical Line Test .”
::要确定一个关系是否是一个函数, 您需要检查一个输入值是否导致两个不同的输出值。 如果一个输入值确实导致两个不同的输出值, 您将能够从视觉上看到两个输出值, 因为两个点会垂直排列。 您通常可以使用所谓的“ 垂直线测试” 来找到这一点 。

播放段落

The vertical line test involves moving a vertical line across a graph from left to right. If the line  ever intersects two points at one $\begin{array}{r}x\text{-}\end{array}$ value,  it  means the same $\begin{array}{r}x\text{-}\end{array}$ value has two different $\begin{array}{r}y\text{-}\end{array}$ values, which in turn means that the relation is not a function.
::垂直线测试涉及将一条垂直线从左向右跨过一个图形。如果一条线在一个 x 值上交叉两个点,这意味着相同的 x 值有两个不同的 y 值,这反过来又意味着关系不是一个函数。

播放段落

Arrange the points in the interactive below and test whether the relation is a function.
::将下文互动部分的点数排列,并测试关系是否是一个函数。

播放段落

Discussion Questions
::讨论问题 讨论问题

播放段落
1. What did you need to do to ensure that the relation was a function?
   ::您需要做些什么来确保这种关系是一个功能?
播放段落
2. What did you need to do to ensure that the relation was not a function?
   ::你需要做些什么来确保这种关系不是一项职能?

播放段落

Use the interactive below to perform the vertical line test on your own.
::使用下面的交互数据进行垂直线测试。