Section outline

  • App Development
    ::App 开发

    App developers use functions daily to monitor the performance of their apps. Special programs provide reports of the performance of the apps over time. These reports include detailed graphs displays active users, app response time, downloads, add revenue , etc. This information is crucial to launching and maintaining a successful app in a competitive field. The success of an app is largely dependent on how it is received by users. Knowledge of how the users experience the app helps developers understand what steps they need to take to provide users with the best experience possible. Developers need to be able to interpret functions and understand what increases, decreases and constants mean in the context of the function graph. These functions will be explored in activity 2 and activity 3.
    ::应用程序开发者每天使用功能监测应用程序的性能。 特殊程序提供应用程序在一段时间内的业绩报告。 这些报告包括详细的图表,显示活跃用户、 应用程序响应时间、 下载、 增加收入等。 这一信息对于在竞争性字段中启动和维护成功应用程序至关重要。 应用程序的成功与否在很大程度上取决于用户如何收到。 了解用户如何体验应用程序有助于开发者了解他们需要采取哪些步骤来向用户提供最佳经验。 开发者需要能够解释函数,并了解在功能图中增加、减少和常数的含义。 这些功能将在活动2和活动3中探讨。

    Understanding a Graph in the Context
    ::理解背景图

    Every function tells a story in context and those stories are useful in many professions. In the previous section, you explored position vs. time graphs. These graphs are related to velocity vs. time graphs since velocity can be determined dividing by time. Velocity is the speed with direction.
    ::每个函数都用上下文来描述一个故事,而这些故事在许多职业中都是有用的。在上一节中,您探索了位置和时间图。这些图表与速度和时间图有关,因为速度可以由时间来决定。速度是随方向的速度。

    Use the interactive below to examine two sample velocity vs. time graphs and break down what happened over the course of the functions.
    ::使用下面的交互数据来检查两个样本速度相对于时间图,并分解在函数过程中发生的情况。

    INTERACTIVE
    Velocity vs. Time Graphs
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    These functions tell us at what position an object is at different points in time.  f ( x )  is represented by the blue function and  g ( x )  is represented by the green function.
    ::这些函数告诉我们一个对象在不同时间点的位置。 f(x) 代表蓝色函数, g(x) 代表绿色函数。

    • Move the red point to change how many seconds have passed.
      ::移动红点以改变已经过了多少秒的时间 。
    • Click "Change Graph" to switch between  f ( x )  and  g ( x ) .  
      ::单击“ 变化图” 在 f( x) 和 g( x) 之间切换。
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    1.

    Over which interval is the velocity of @$\begin{align*}f(x)\end{align*}@$ decreasing?
    ::@ $\ begin{ align} f( x)\ end{ aliign} $ 正在递减的速度是多少间隔 ?

    a

    20-100

    b

    0-20

    c

    100-120

    d

    120-160

    Create a Function
    ::创建函数

    You can make assumptions about a function based on the at various points.
    ::您可以根据各个点对函数作出假设。

    • A positive slope means that the outputs are increasing. 
      ::积极的斜坡意味着产出正在增加。
    • A negative slope means that the outputs are decreasing. 
      ::负斜坡意味着产出正在减少。
    • A slope of 0 means that the outputs are constant .
      ::0的斜坡意味着产出是不变的。

    C onstruct a function to represent the following situation:
    ::构造一个函数以代表以下状态:

    An app developer is looking at a graph which shows active users as a function of time. This means that the input value is the time and the output value is the number of people using the app at that time. The time 0 hours represents 12:00 AM EST. The graph shows that from 0 hours to 7 hours, the number of users stays constant at 600. From 7 hours to 12 hours, the number of users increases to 2,000. The number of users stays constant at 2,000  until 20 hours at which point the number of users decreases to 800 at 24 hours.
    ::应用程序开发者正在查看一个显示活跃用户时间函数的图表。 这意味着输入值是时间, 输出值是使用该应用程序的人数。 0小时代表 AM EST 的 12 点。 该图显示, 从 0 小时到 7 小时, 用户数量保持在600 小时不变。 从 7 小时到 12 小时, 用户数量增加到 2 000 小时。 用户数量保持在 2 000 小时到 20 小时, 用户数量在 24 小时下降到 800 。

    Construct this function below.
    ::在下面构造此函数 。

    INTERACTIVE
    Create a Function
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    Move the red points to show the usage of the app over time:
    ::移动红点以显示应用程序随时间演变的使用情况 :

    • From 0 to 7 hours, there are 600 users
      ::0至7小时,有600个用户
    • From 7 to 12 hours, usage increases to 2,000 users
      ::从7小时到12小时,使用量增加到2 000个用户
    • From 12 to 20 hours, usage is maintained at 2,000 users
      ::12至20小时的使用量维持在2 000个用户
    • From 20 to 24 hours, usage decreases to 800 users
      ::从20小时到24小时,用户减少至800个用户
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    Discussion Questions
    ::讨论问题 讨论问题

    1. What information can the app developer take from this function graph?
      ::App 开发者可以从此函数图中获取什么信息 ?
    2. What kind of app do you think this is?
      ::你觉得这是什么应用?

       

    What’s That App?
    ::什么是App?

    Look at the user activity function graph below. In dependently , construct a story of an app which would have this user activity be sure to explain any increases, decreases, and constants.
    ::查看下面的用户活动函数图。 独立地, 构建一个有此用户活动的应用程序的故事, 可以解释任何增加、 减少和常数 。

    INTERACTIVE
    What's That App?
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    Move the red points to show the usage of the app over time:
    ::移动红点以显示应用程序随时间演变的使用情况 :

    • From 0 to 6 hours, 200 users
      ::0至6小时,200个用户
    • From 6 to 9 hours, usage increases to 1000 users
      ::6至9小时,使用量增加至1 000个用户
    • From 9 to 11 hours, usage decreases to 800 users
      ::9至11小时,使用量减至800个用户
    • From 11 to 15 hours, 800 users
      ::11至15小时,800个用户
    • From 15 to 21 hours, usage increases to 1800 users
      ::从15小时到21小时,使用量增加到1 800个用户
    • From 21 to 24 hours, usage decreases to 200 users
      ::用户从21小时减少到24小时,使用次数从21小时减少到24小时,减少到200个用户
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      Summary
    • When interpreting the graph of a function:
      • A positive slope means that the outputs are increasing. 
        ::积极的斜坡意味着产出正在增加。
      • A negative slope means that the outputs are decreasing. 
        ::负斜坡意味着产出正在减少。
      • A slope of 0 means that the outputs are constant.
        ::0的斜坡意味着产出是不变的。

      ::当解释函数的图形时:正斜度表示产出在增加。负斜度表示产出在减少。0斜度表示产出不变。