(i) Constant Function:
A function is said to be a constant function if there is a real number
such that
.
Hence which is singleton.
Example:
, the line parallel to
.
(ii) Identify function:
For any non-empty set , the function
is defined by
is called the identity function on
. It is denoted by
.
Hence
The line plotted through origin.
(iii) Polynomial Function:
A function defined by
, where
is a non-negative integer and
are real constant with
, is called a polynomial function or a polynomial of degree
.
Example:
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(iv) Rational Function:
A function , where
&
are polynomials with
, is called a rational function.
Example:
,
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(v) Modulus function:
If is defined by
is called Modulus function.
The modulus function is also known as absolute value function.
Its domain
and rage is
Example:
(vi) Signum function:
The signum function on is defined by
The range of is
.
(vii) Exponential function:
An exponential function is defined by
.
The fact that exists for every
.
Example:
(a)
(b)
(c) If
(d) If then
(e) is closer to the
-axis as
recedes away from zero along negative values.
and
(viii) Logarithmic function:
The function defined by
where
is called the logarithmic function.
The graphs meets the -axis at
and never meet the
– axis.
Some Logarithmic function:
(a)
(b)
(c)
(d)
(e)
(f)
(g) If and if
(h)
(ix) Greatest Integer Function:
The function is defined by
where is the greatest integer not greater that
(less than or equal to
) is called the greatest integer function.
(a)
and
The graph consists of infinitively many closed open parallel line segments.