Introduction to algebra function form

In algebra, a function is informally a function that satisfies a polynomial equation whose coefficients are themselves polynomials. For example, an algebra function is in the form of one variable x is a solution y for an equation,

an(x)yn + an-1(x)yn-1 + ... + a0(x)= 0

where the coefficients ai(x) are polynomial functions of x. A function which is not algebraic is called a transcendental function. (Source: From Wikipedia).

Here we are going to study about algebra functions and their standard forms.

 

Standard form of an algebra function

 

An algebra function is in the form of,

                  an(x)yn + an-1(x)yn-1 + ... + a0(x) = 0

Where, an, an-1, a0 are coeffiecients.

The highest power of a term in a algebra function is called as the degree of the function. An algebra function can be classified by degree as follows,

A function with degree 0 is called as constant.

A function with degree 1 is called as linear function.

A function with degree 2 is called as quadratic function.

A function with degree 3 is called as cubic function.

A function with degree 4 is called as quartic function.

 

Example problems

 

Example 1

Solve the function for x, x + 2 = 3 - 2x

Solution

x + 2 = 3 - 2x

Add 2x on both sides

x + 2 + 2x = 3 - 2x - 2x

3x + 2 = 3

Subtract 2 on both sides,

3x + 2 - 2 = 3 - 2

3x = 1

Divide by 3 on both sides,

`(3x)/3` = `1/3`

x = `1/3`

 

Example 2

Solve the system of linear functions,

x + 2y = 3 and y = x + 2

Solution

x + 2y = 3 ------------ 1

y = x + 2   ------------ 2

Plug equation 2 in equation 1,

x + 2(x + 2) = 3

x + 2x + 4 = 3

3x + 4 = 3

3x + 4 - 4 = 3 - 4

3x = -1

x = `-1/3`

Plug x = `-1/3` in equation 2

y = `-1/3` + 2

    = `-1/3` + `6/3`

    = `(-1 + 6)/3`

  y = `5/3`

So, the solution of the given system of algebra functions, x = `1/3` and y = `5/3`