### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Some real functions and their graphs

(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:

(iv) Rational Function:

A function , where & are polynomials with , is called a rational function.

Example:

,

(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.

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