Symbols are
used as a
concise way of
giving lengthy
instructions
related to
numbers and
logic.
Math Symbols are
a communication
tool. Symbols are an
invention which is
used to eliminate
the need to write
long, plain language
instructions to
describe
calculations and
other processes.
The most
valuable, most
frequently used
Symbols in
mathematics . .
.:
The
most important, most
frequently used
Miscellaneous
symbols are listed
below.
Math
Notation for
the
"Function"
of x

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The Function
Notation
f(x)
means two
things:
(1)
f(x)
literally means
that the
value of
f(x) depends
upon the value
of
x.
And .
. .
(2)
For every value
of x, there is
only
one
unique value
f(x).
f(x)
is often
used
interchangeably
with
y.
Most of the
time this is
OK, but
y is not
the same as
f(x).
f(x)
is a function.
f(x)
always
satisfies both
of the criteria
listed as (1)
and (2), shown
above.
Y may
or may not
represent a
function. It
may only
satisfy the
criteria listed
as (1).
Example
1:
f(x),
function
of x (can
be used
interchangeably
with the
y
in this
example)
y = x +
1
f(x) = x +
1
if x =
4
y = 4 +
1
y =
5
f(4) = 4 +
1
f(4) =
5
Note:
both
y and
f(x)
represent
a
function.
Both
notations
satisfy
the
criteria
for
(1)
and
(2)
above.
Note:
both
y
and
f(x)
=
5.
Example
2:
y,
the
following
relation
is
not a
function
Note:
there
are
two
values
of y
for
every
value
of x.
A
function
can
have
only
one
value
of y
for
each
value
of x.
Therefore,
this
is
not a
function.