Game Development Reference
In-Depth Information
g. (---6, 7)
h. (1, ---6)
i. (2, 2)
j. (---2, ---2)
Functions
A function results when you discover a relationship between the values in a
domain and the values in a range. Certain limitations apply to this relation-
ship, however. First, each domain value must be unique. Second, each range
value must correspond to only one domain value. Expressed differently, if you
designate a number in the domain, then you find only one number in the
range that corresponds to it. In this respect, since a one-to-one correspon-
dence pertains between the values in the domain and the values in the range,
the value of the number in the domain
determines
the value of the number in
the range.
In Figure 4.10, a Cartesian system allows you to illustrate the functional rela-
tionship. This function establishes a pattern that relates the values of the domain
with those of the range. The domain and range constitute sets. While the
numbers in the domain form a union with the numbers in the range, it remains
that the domain-range pairs that result are all unique. The equation that gen-
erates these pairs is
y ¼ x þ
1.
Given this equation, then, each value you designate for the domain generates a
unique value. The equation, then, is a proper function. It is an equation or
relationship that allows you to generate unique range values by using a set of
domain values that are themselves unique. No two domain values generate the
same range value.
Non-Functional Relationship
Not every pair of sets designating a domain and a range represent a functional
relationship. One test you can use to determine whether the graphical depiction
of a set of coordinates represents a function involves using a vertical line.
Accordingly, if you apply the vertical line test to a graph, the graph cannot pass
over the line more than once.
