微积分网课代修|预备微积分代写precalculus辅导|MATH1710 Evaluating a Function Given in Tabular Form

微积分网课代修|预备微积分代写precalculus辅导|MATH1710 Evaluating a Function Given in Tabular Form

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微积分网课代修|预备微积分代写precalculus辅导|MATH1710 Evaluating a Function Given in Tabular Form

微积分网课代修|预备微积分代写precalculus辅导|Evaluating a Function Given in Tabular Form

As we saw above, we can represent functions in tables. Conversely, we can use information in tables to write functions, and we can evaluate functions using the tables. For example, how well do our pets recall the fond memories we share with them? There is an urban legend that a goldfish has a memory of 3 seconds, but this is just a myth. Goldfish can remember up to 3 months, while the beta fish has a memory of up to 5 months. And while a puppy’s memory span is no longer than 30 seconds, the adult dog can remember for 5 minutes. This is meager compared to a cat, whose memory span lasts for 16 hours.

The function that relates the type of pet to the duration of its memory span is more easily visualized with the use of a table. See Table $10 .^{[2]}$

At times, evaluating a function in table form may be more useful than using equations. Here let us call the function $P$. The domain of the function is the type of pet and the range is a real number representing the number of hours the pet’s memory span lasts. We can evaluate the function $P$ at the input value of “goldfish.” We would write $P($ goldfish $)=2160$. Notice that, to evaluate the function in table form, we identify the input value and the corresponding output value from the pertinent row of the table. The tabular form for function $P$ seems ideally suited to this function, more so than writing it in paragraph or function form.

微积分网课代修|预备微积分代写precalculus辅导|Determining Whether a Function is One-to-One

Some functions have a given output value that corresponds to two or more input values. For example, in the stock chart shown in Figure 1 at the beginning of this chapter, the stock price was $\$ 1,000$ on five different dates, meaning that there were five different input values that all resulted in the same output value of $\$ 1,000$.

However, some functions have only one input value for each output value, as well as having only one output for each input. We call these functions one-to-one functions. As an example, consider a school that uses only letter grades and decimal equivalents, as listed in Table $12 .$

This grading system represents a one-to-one function, because each letter input yields one particular grade point average output and each grade point average corresponds to one input letter.

To visualize this concept, let’s look again at the two simple functions sketched in Figure 1(a) and Figure 1(b). The function in part (a) shows a relationship that is not a one-to-one function because inputs $q$ and $r$ both give output $n$. The function in part (b) shows a relationship that is a one-to-one function because each input is associated with a single output.
one-to-one function
A one-to-one function is a function in which each output value corresponds to exactly one input value.

微积分网课代修|预备微积分代写precalculus辅导|MATH1710 Evaluating a Function Given in Tabular Form

微积分网课代修|预备微积分代写precalculus辅导|Evaluating a Function Given in Tabular Form

正如我们在上面看到的,我们可以在表格中表示函数。相反,我们可以使用表中的信息来编写函数,并且可以使用表来评估函数。例如,我们的宠物对我们与它们分享的美好回忆的回忆程度如何?有一个都市传说,金鱼有3秒的记忆,但这只是一个神话。金鱼最多可以记住 3 个月,而 Beta 鱼最多可以记住 5 个月。虽然小狗的记忆跨度不超过 30 秒,但成年狗可以记住 5 分钟。与记忆持续 16 小时的猫相比,这是微不足道的。

使用表格更容易将宠物类型与其记忆跨度的持续时间相关联的函数可视化。见表10.[2]

有时,以表格形式评估函数可能比使用方程式更有用。这里让我们调用函数磷. 该函数的域是宠物的类型,范围是一个实数,表示宠物的记忆跨度持续的小时数。我们可以评估函数磷在“金鱼”的输入值处。我们会写磷(金鱼)=2160. 请注意,为了以表格形式评估函数,我们从表格的相关行中识别输入值和相应的输出值。函数的表格形式磷似乎非常适合此功能,而不是以段落或功能形式编写它。

微积分网课代修|预备微积分代写precalculus辅导|Determining Whether a Function is One-to-One

某些函数具有对应于两个或多个输入值的给定输出值。例如,在本章开头图 1 所示的股票图表中,股票价格为$1,000在五个不同的日期,这意味着有五个不同的输入值都导致相同的输出值$1,000.

但是,有些函数的每个输出值只有一个输入值,以及每个输入只有一个输出。我们将这些函数称为一对一函数。例如,考虑一所只使用字母等级和十进制等值的学校,如表中所列12.

该评分系统表示一对一的函数,因为每个字母输入产生一个特定的平均绩点输出,并且每个平均绩点对应于一个输入字母。

为了形象化这个概念,让我们再看一下图 1(a) 和图 1(b) 中描绘的两个简单函数。(a) 部分中的函数显示了一个不是一对一函数的关系,因为输入q和r都给出输出n. (b) 部分中的函数显示了一对一函数的关系,因为每个输入都与单个输出相关联。
一对一函数
一对一函数是一种函数,其中每个输出值恰好对应一个输入值。

微积分网课代修|预备微积分代写precalculus辅导|MATH1710 Evaluating a Function Given in Tabular Form
微积分网课代修|预备微积分代写precalculus辅导

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