If you continue browsing this website, you agree to our policies:

x
Completion requirements

Read this section for an introduction to functions and their graphs. Work through practice problems 1-5.

The **graph **of a numerical function consists of a plot of ordered pairs where is in the domain of and . A table of values of a numerical function consists of
a list of some of the ordered pairs where . Fig. shows a graph of for .

A function can be defined by a graph or by a table of values, and
these types of definitions are common in applied fields. The outcome of an experiment will depend on the input, but the experimenter may not know the "rule" for predicting the outcome. In that case, the experimenter
usually represents the experiment function as a table of measured outcome values verses input values or as a graph of the outcomes verses the inputs. The table and graph in Fig. 3 show the deflections obtained when weights are loaded
at the end of a wooden stick. The graph in Fig. 4 shows the temperature of a hot cup of tea as a function of the time as it sits in a 68^{o} F room. In these experiments, the "rule" for the function is that actual
outcome of the experiment.

Tables have the advantage of presenting the data explicitly, but it is often difficult to detect patterns simply from lists of numbers. Graphs tend to obscure some of the precision of the data, but patterns
are much easier to detect visually - we can actually see what is happening with the numbers.