导言:关系和职能

In a previous chapter, we discussed linear equations and linear inequalities, like $\begin{align*}y=2x+3\end{align*}$  and $\begin{align*}y>2x+3\end{align*}$ . When  we choose a value for $\begin{align*}x\end{align*}$ , say 4, the equation only has one solution: $\begin{align*}y=11\end{align*}$ . On the other hand, the inequality has  an infinite number of solutions. When  $\begin{align*}x=4\end{align*}$ , $\begin{align*}y>2(4)+3=11\end{align*}$ ; $\begin{align*}y\end{align*}$  could be 12 or 13 or 14 or any number greater  than 11. The difference in the number of solutions for a particular value of $\begin{align*}y\end{align*}$  is the difference between a relation and  a special type of relation called a function.
::在前一章中,我们讨论了线性方程和线性不平等,如y=2x+3和y>2x+3。当我们选择 x 的值时,比如 4, 方程只有一个解决方案: y=11。 另一方面, 不平等有无限数量的解决方案。 当 x=4, y>2(4)+3=11; y 可能为 12 或 13 或 14 或 任何大于 11 的数值时, y 特定值的解决方案数目的差别是 关系和 被称为函数的特殊类型关系之间的差别 。

Functions are used to model real-world phenomena in a variety of subjects and have special properties that you will explore in future math classes. In this chapter, we will focus on the basics of functions—identifying them, the possible input values and output values, function notation, and reading their graphs. We will also consider direct, indirect, and joint variation.

::函数用于模拟各种科目的现实世界现象,并具有在未来数学课中将探索的特殊特性。 在本章中,我们将侧重于函数的基本特征 — — 识别它们、可能的输入值和输出值、函数符号和阅读它们的图表。我们还将考虑直接、间接和共同的变异。

By the end of this chapter, you should be able to:    
::在本章末尾,你应当能够:

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• Identify whether a relation is or is not a function.    
  ::确定关系是否为函数。
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• Use the Vertical Line Test to identify graphs of functions.    
  ::使用垂直线测试来识别函数的图形。
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• Determine the domain and range of a function.    
  ::确定函数的域和范围。
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• Use function notation to evaluate a function.    
  ::函数符号用于评价函数。
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• Identify where a function is increasing, decreasing, or constant.    
  ::确定一项职能在增加、减少或常数。
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• Identify the global/absolute and local/relative extrema.
  ::确定全球/绝对和地方/相对极端。
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• Recognize transformations of functions.
  ::承认职能的转变。
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• Recognize direct, indirect, and joint variation.
  ::承认直接、间接和联合差异。

Features      
::特征特征

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• Section 1: Couch Potato    
  ::第1节:土豆沙袋
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• Section 3: Catching Your Breath    
  ::第3节:抓住你的呼吸
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• Section 4: Splines: The Truth Behind Video Games
  ::第4节:短条:视频游戏背后的真相
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• Section 9: Good Vibrations
  ::第9节:良好振动

Connections    
::连接连接

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• Modeling the Grand Staircase Over Time    
  ::长期建模大楼梯
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• What Are We Reading?
  ::我们在读什么?