A powerful feature of Excel is that the
contents of a worksheet cell can be made to depend on variables
in other cells. The relation between the dependent cell
and the independent variable cells is called a function.
In mathematical terms, the value of y depends
of the values of the variables in the vector x according
to the function f.
We restrict attention to cases in which x is
a vector of one or more independent variables. Independent
variables are continuous and bounded with simple lower
and upper bounds. The function f(x)
is a single value, a scalar, that depends on the values
of the variables. The only immediate restriction on f(x)
is that it be defined and finite for all values of x in
a specified range. An example is the function:
Although this is a very simple function, Excel allows
an almost infinite variety using its built-in functions
combined in various arrangements by formulas provided by
the user. We require that the value of the dependent variable
be placed in a single cell on the worksheet, but that cell
can depend on any number of other cells on the worksheet
or on cells anywhere in the Excel workbook. Although all
the examples in this section involve functions that have
closed form expressions and are relatively easy to evaluate,
the more useful situation is where the function is the
result of a series of computations in an Excel workbook.
That function may take considerable time to evaluate for
a given selection of x.