**More Topics on Functions**

What is a Function in Math
Algebra is a vast subject which includes everything from elementary equation solving to the study of abstractions like groups, fields etc. The basic study of algebra are called elementary algebra, the abstract portions are called abstract algebra or the current algebra. Elementary algebra is necessary for any study of mathematics, science ,engineering, medicine and economics. The elementary algebra is often part of the curriculum in secondary education and introduces the concept of variables representing numbers. Variables are managed using the rules of operations that apply to numbers such as addition and subtraction.

Abstract algebra is an important part in advanced mathematics, studied basically by professional mathematicians.

## Algebraic Funstions

Algebraic function is a root of polynomial equation. It can
also be defined as a function that fulfils algebraic equations. It involves all
algebraic operations like addition, subtraction, multiplication, division and
raising to a rational power.The function f(x) is
algebraic if y = f(x) is a solution of an equation of the form Pn(x)yn+...............+P1(x)y+P0(x) = 0.

## Types of Algebraic functions

1. Linear functions - the general linear equation can be defined as
f(x)=ax+b

2. Quadratic function - the general quadratic equation can be defined as f(x) = ax^{2} + bx + c, a = 0.

3. Cubic Function - the general equation of cubic function is f(x) = ax^{3} + bx^{2} + cx + d, a = 0.

4. Rational Function - the function written in the form of a/b is called
rational function f(x) = p(x)q(x)

5. Polynomial Function - is the sum of monomials f(x)
= anxn+an-1xn-1+..............+a2x2+a1x+a0

6. Radical Function- are functions which have roots f(x) = p(x) sqr root n.

7. Trigonometric function - A function f(x)=sinx, f(x)=cosx, etc then the function f(x) is called
the trigonometric function.

8. Exponential function - any function in which variables appear as
power or exponent is called exponential function. For example f(x)=a^{x}

9. Logarithmic function - any function in which the variables appear
as argument is called logarithmic function. For example f(x)=log_{a}(x)

## Examples of Algebraic
functions

Some of the examples
are solved

**Question 1:**** **If f(x) = x + 1, then find
the values of f(0) and f(2).

**Solution:**

Given f(x) = x + 1 .............(i)

Find f(0) and f(2)

Plug x = 0 in (i)

=> f(0) = 0 + 1 = 1

=> f(0) = 1

Again, plug x = 2 in (i)

=> f(2) = 2 + 1 = 3

=> f(2) = 3.

**Question 2:**** **Find the factors of f(x) = 2x^{2} + 4x - 12.

**Solution:**

Given 2x^{2} + 4x - 12

Factor the GCD

=> 2x^{2} + 4x - 12 = 2(x^{2} + 2x - 6)

Factor the quadratic, x^{2} + 2x - 6

x^{2} + 2x - 6 = x^{2} + 3x - 2x - 6

= x(x + 3) - 2(x + 3)

= (x - 2)(x + 3)

=> Factors of 2x^{2} + 4x - 12 = 2 (x - 2)(x + 3)