Math 1310 Class Notes – Section 3.1, Page 1 of 6
Math 1310
Section 3.1
Functions – Basic Ideas
The rest of this course deals with
functions.
A
function
f
is a rule that assigns to each element in a set
A
one and only one element of
a set
B
.
The set
A
is called the
domain
of
f
.
Sets
A
and
B
are sets of real numbers.
Functions are so important that we use a special notation when working with them.
We’ll
write
f
(
x
) to denote the value of function
f
at
x
.
We read this as “
f
of
x
.” The
range
of a
function is all of the possible values of the function as
x
varies through the numbers in the
domain.
We can use letters other than
f
to denote a function, so you may see a function
such as
).
(
or
)
(
),
(
x
P
x
h
x
g
We can show a relationship between two sets of numbers using a
mapping
.
We can answer several questions using a mapping, such as:
Does the mapping represent a function?
If so, what is the domain of the function?
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 Summer '08
 MARKS
 Sets, Continuous function, Category theory, Domain of a function, codomain

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