# Important Functions

1.**Absolute value function (modulus function):**

= magnitude of or the positive value of .

The expression can be further split as follows:

=

**Continuity**

The graph of is continuous (i.e. no break in the curve) but has a corner at origin as shown.

**Domain & Range**

The Domain of the function is and Range is

# Greatest integer function (unit step function)

= the greatest integer less than or equal to .

It can also be simplified as:

if where n is an integer.

**Continuity **

The graph of f (x) is discontinuous (i.e. break in the curve) at integral value of x.

**Domain & Range**

The Domain of the function is and Range is

# Signum Function

=

This can also be written as

=

**Continuity**

The graph of is continuous for all values of except at where there is a break in the curve.

**Domain & Range**

The Domain of the function is and Range is set

# Exponential Function

where or

This function is the inverse of logarithmic function i.e. it can be obtained by interchanging by in

As observed from the graph, if then increases as increases.

If, then decreases as increases.

**Continuity**

The graph of is continuous (i.e. no break in the curve) everywhere.

**Domain & Range**

The Domain of the function is and Range is.

# Trigonometric Functions

If a function

**Period**

Period of and is

Period of is

**Continuity**

The graph of and is continuous (i.e. no break in the curve) everywhere.

The graph of is discontinuous (i.e. break in the curve) at x = (2n + 1)

**Domain & Range**

The Domain of is and Range is set [-A, A].

The Domain of is and Range is.