** Most Important Types of functions** **are**

Some important types are **functions **are given below:

**Algebraic Function Definition Short**

Algebraic function are those functions which are defined by algebraic expressions.

**Linear functions Short Definition With Example**

If the degree of polynomial function is 1, then it is called a **linear function**. linear function is of the form:

** f(x) = ax + b** (a not equal to 0) a, b, are the real numbers.

for example f(x) = 3x + 4 or y = 3x + 4 is a** linear function**. its domain and range are the set of real number.

**Identity of Trigonometric Functions**

For any set X, a function** I : X → X** of the form** I(x) = x ∀ x 𝛜 X,** is called an** identity function**. its domain and range is the set X itself. in particular, if X = r then **I(x) = x** for all** x 𝛜 R,** is the identity function.

**Constant Function Examples and Definition**

Let X and Y be sets of real numbers. A function **C : X → Y** defined by** C(x) = a, ∀ x 𝛜 X , a 𝛜 Y** and defined by is called a constant function. for example, **C: R → R** defined by** C(x) = 2 , ∀ x 𝛜 R **is a **constant function**.

**What is Rational ****functions** in Math?

**functions**in Math?

A function R(x) of the form **P(x)/Q(x)**, were both** P(x)** and** Q(x)** are polynomial functions and **Q(x) ≠ 0** is called a rational function. The domain of a rational **function** R(x) is the set of all realm numbers x for which **Q(x) ≠ 0.**