text: # 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|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.