Graphical Representation of a Function
The function f : R  {0} → R is represented in the graph such that the x coordinate represents the independent variable and the y coordinate represents the dependent variable. The graph of the function shows various properties of the function directly and more clearly. The limiting case of the graph of the function is represented by an asymptote:
Asymptote is a straight line to which graph of the function approaches at infinity but does not exactly touch it as shown in figure shown above.
Coordinate axis x = 0 is asymptotes to the graph of y = 1/x.
We consider some examples of functions and their graphs
S.No.

FUNCTION

DOMAN, RANGE AND DEFINITION

GRAPH

1.

A Constant Function

f : R → {c}
defined by f{x} = c


2.

The Identity Function

f : R → R
defined by f(x) = x


3.

The Absolute Value Function

f : R → [0, ∞)
defined by f(x) = x


4.

The Exponential Function

f : R → (0, ∞)
defined by f(x) = e^{x}


5.

The Natural Logarithmic

f: (0, ∞) → R
defined by f(x) = In x


6.

The Greatest Integer Function

f : R → Z
defined by f(x) = [x]
the greatest integer < x


7.

The Fractional part of x

f : R → R
defined by f(x) = {x}


8.

Polynomial Functions

f(x) = a_{0}x^{n} + a_{1}x^{n1} + .... + a^{n1} x + a_{n}
where a_{0}, a_{1}, ......, a_{n} are real numbers, a_{0} ≠ 0.

9.

Rational Functions

f(x) = p(x)/q(x), where p(x) and q(x) are polynomials in x. Domain is R  {x : q(x) = 0}

10. Trigonometric or Circular Functions:
11. Inverse circular Functions
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