GRAPHING CALCULATORS AND COMPUTERS
In this section we assume that you have access to a graphing calculator or a computer with
graphing software. We will see that the use of such a device enables us to graph more com-
plicated functions and to solve more complex problems than would otherwise be possible.
We also point out some of the pitfalls that can occur with these machines.
Graphing calculators and computers can give very accurate graphs of functions. But we
will see in Chapter 4 that only through the use of calculus can we be sure that we have
uncovered all the interesting aspects of a graph.
A graphing calculator or computer displays a rectangular portion of the graph of a func-
tion in a display window or viewing screen, which we refer to as a viewing rectangle.
The default screen often gives an incomplete or misleading picture, so it is important to
choose the viewing rectangle with care. If we choose the -values to range from a mini-
mum value of
to a maximum value of
and the -values to range from
a minimum of
to a maximum of
, then the visible portion of the graph
lies in the rectangle
shown in Figure 1. We refer to this rectangle as the
by
viewing rectangle.
The machine draws the graph of a function much as you would. It plots points of the
form
for a certain number of equally spaced values of between and . If an
-value is not in the domain of , or if
lies outside the viewing rectangle, it moves on
to the next -value. The machine connects each point to the preceding plotted point to form
a representation of the graph of .
EXAMPLE 1 Draw the graph of the function
in each of the following view-
ing rectangles.
(a)
by
(b)
by
(c)
by
(d)
by
SOLUTION For part (a) we select the range by setting min
, max
, min
and max
. The resulting graph is shown in Figure 2(a). The display window is
blank! A moment’s thought provides the explanation: Notice that
for all , so
for all . Thus, the range of the function
is
. This means
that the graph of
lies entirely outside the viewing rectangle
by
.
The gra