7.4 职能的等等同-interactive

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  职能之平

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  Function Notation
  ::函数符号

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  Every programming language has a specific way to write functions, and the language of mathematics is no different. Y ou have seen functions represented as a set of ordered pairs, in a table, as a mapping diagram, and on a graph. Functions can also be written using an equation . When equations are used to represent a function , they  are usually written in a specific way called function notation.
  ::每个编程语言都有写函数的具体方式,而数学的语言也是一样的。您已经看到函数代表了一组有顺序的对子,在表格中,在图表中,在图表中,在图表中。函数也可以用方程式来写。当方程式用于代表函数时,它们通常以特定的方式写成,称为函数符号。

  

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  In the example above ,  the letter $\begin{array}{r}f\end{array}$  is the name of the function. There will be situations  that require more than one function, and nam ing  the functions helps to identify specific ones . Not every function will be named using the letter  $\begin{array}{r}f.\end{array}$  Other common function names include $\begin{array}{r}g,h,p,\text{and }s.\end{array}$  Often, the letter chosen as a function name relates to the output, such as using the letter  $\begin{array}{r}v\end{array}$  to name a  velocity function, or  $\begin{array}{r}d\end{array}$  to identify a distance function.
  ::在上述示例中,字母 f 是函数的名称。 会出现需要多个函数的情况, 命名函数有助于识别具体函数。 不是每个函数都会用字母 f 命名。 其他常见函数名称包括 g、 h、 p 和 s. 通常, 以函数名称选择的字母与输出有关, 例如使用字母 v 命名速度函数, 或 d 来识别距离函数 。

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  The $\begin{array}{r}x\end{array}$  lets the user know where to put the input value. The expression $\begin{array}{r}x-5\end{array}$  represents the output value, and describes what the function does (in this case, "take the input, and subtract 5 from it"). Since $\begin{array}{r}x-5\end{array}$  is equal to $\begin{array}{r}f(x),\end{array}$  being asked to find $\begin{array}{r}f(x)\end{array}$  means to find the output.
  ::x 让用户知道将输入值放在哪里。 表达式 x- 5 代表输出值, 并描述函数的作用( 在此情况下, “ 获取输入, 从中减去 5 ) 。 因为 x- 5 等于 f( x) , 需要找到 f( x) 的输出方式 。

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  Calculating Outputs
  ::计算产出

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  When you want to put a value into the function, you substitute it in for $\begin{array}{r}x.\end{array}$  Writing $\begin{array}{r}f(7)\end{array}$  means to substitute 7 into the equation, and find the output when $\begin{array}{r}x=7.\end{array}$  If the output simplifies to 2, then we say that $\begin{array}{r}f(7)=2.\end{array}$  The statement $\begin{array}{r}f(7)=2\end{array}$  means that when you input 7 into the function, the output will be 2. This statement can also be written as the coordinate (7, 2).
  ::当您想要在函数中输入一个值时,您可以将其替换为 x。写入 f(7) 意味着在方程中替换 7, 并在 x=7 中找到输出, 如果输出简化为 2, 那么我们说 f(7)=2 。 语句 f(7)=2 意味着当您输入 7 函数时, 输出将是 2 。 这个语句也可以作为坐标( 7, 2) 写入 。

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  Use the interactive below to explore the idea of substituting a value into a function.
  ::使用下文的互动来探讨将值替换为函数的想法。

  

  INTERACTIVE

  Calculating Outputs

  

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  • Move the slider to change the value of  $x.$  
    ::移动滑块以更改 x 的值。
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  • Choose a function with the buttons below.
    ::选择以下按钮的函数。
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  • See the output calculated based on the input and the function.
    ::见根据输入和函数计算的产出。

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  Using Equations to Find Outputs
  ::使用查找产出的等量

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  If you didn't already, you may wish to refer to t he lesson  to  explore how to write a rule for a function. These rules can be written as equations.  You can also use equations to write verbal descriptions of functions.
  ::如果您还没有, 您也许想参考该课来探索如何为函数写入规则。 这些规则可以作为等式来写。 您也可以使用等式来写函数的口头描述 。

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  Example
  ::示例示例示例示例

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  Tom is driving in his car at the constant speed of 30 miles per hour. Write a function to show the distance  the car traveled  in miles after $\begin{array}{r}x\end{array}$  hours.
  ::汤姆正以每小时30英里的恒定速度驾驶他的车。 写一个函数来显示汽车在x小时后行驶的距离 。

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  You  may have encountered problems quite similar to this in the lesson , where you  would have  written equations to represent proportional and linear relationships. In the driving example here, you are dealing with a proportional relationship, because at 0 hours, Tom has traveled 0 miles. The constant of proportionality is 30, which gives you the equation $\begin{array}{r}y=30x.\end{array}$   You can write it as a function equation by simply replacing the $\begin{array}{r}y\end{array}$  with an $\begin{array}{r}f(x).\end{array}$  Both equations represent a relation with an input and output, but using function notation identifies the relation as a function.
  ::您可能遇到过类似课程中的类似问题, 即您会用书面方程式来代表比例和线性关系。 在此处的驱动示例中, 您正在处理比例关系, 因为 Tom 是在 0 小时行驶了 0 英里。 比例的常数是 30 英里 , 给您以 y= 30x 。 您可以简单地用 f( x) 替换 y 来写成函数方程式。 两种方程式都代表了输入和输出的关系, 但使用函数符号将关系识别为函数 。

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  Answer:  $\begin{array}{r}f(x)=30x\end{array}$
  ::答复:f(x)=30x

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  Answer the questions  below to match descriptions of functions with  appropriate  equations.
  ::回答下列问题,使职务说明与适当的等式相匹配。

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  Writing and Interpreting Equations
  ::书写和口译

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  Use the interactive below to explore equations of functions in the real-world context of nutrition labels.
  ::利用以下互动方式探讨营养标签在现实世界背景下的各种功能的方程式。

  

  INTERACTIVE

  Soda Sugar Table

  

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  Tom's class creates a table to show how the number of sugar packets relates to grams of sugar. Help Tom's class complete the table.
  ::Tom的班级创建了一个表格, 显示糖包的数量与糖克的关系。 帮助 Tom 的班级填满桌子 。

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  • Fill in the table to learn the relationship between the number of packets of sugar and the amount of sugar they contain.
    ::填写表格,了解糖包数量与糖含量之间的关系。
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  • If you have  $x$  packets, how many grams of sugar do you have?
    ::如果你有x包,你有多少克糖?

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     Summary
  ::摘要

  

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  A function may be named with any letter you wish, but the most common are f,g,and h.The x term is replaced by the input value that you want to determine the output value for. The function statement f(x)=x−5 is read as "The function f, performed on the value x, is equal to x−5."
  ::函数可以用您想要的任何字母命名, 但最常见的是 f. g. 和 h. 。 x 术语被您想要确定输出值的输入值所取代。 函数对数 f( x) =x- 5 读作“ 以值 x 执行的函数 f, 等于 x- 5 ” 。