Answer:
Y is a function of X if variable X can assume a correspondence to one or more values of Y. If only one
value of Y corresponds to each value of X, then we say that Y is a single-valued function if X (also
called a “well-defined function”); otherwise Y is called a multivalued function of X. Our secondary
school curriculum assumes that we mean a well-defined function, when functions are discussed, and
we refer to multivalued functions as relations. All of the definitions above also assume that we are
referring to binary relations (i.e. relations of two variables). The input variable (or independent
variable) is usually denoted by x in mathematics, and the output variable (or dependent variable) by
y. The set of all values of x is called the domain and the set of all values of y, the range. As is the case
with one variable statistics, the variables can be discrete or continuous.
The function dependence or correspondence between variables of the domain and the range can be
depicted by a table, by an equation or by a graph. In most investigations, researchers attempt to find
a relationship between the two or more variables. We will deal almost exclusively with relations
between two variables here. For example the circumference of a circle depends (precisely) on its
radius; the pressure of a gas depends (under certain circumstances) on its volume and temperature; the
weights of adults depend (to some extent) on their heights. It is usually desirable to express this
relationship in mathematical form by finding an equation connecting these variables. In the case of the
first two examples, the relationship allows for an exact determination (at least in theory as far as
mathematicians are concerned, and within specified error limits as far as scientists are concerned).
Virtually all “real life” investigations generate statistical or probability relationships (like the latter
example above) in which the resulting function produces only approximate outcomes. Much of our
statistical analysis is concerned with the reliability the outcomes when using data to make predictions
or draw inferences.
Explanation:
hope it helps ^^
