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,

a_{n}(x)y^{n} + a_{n-1}(x)y^{n-1} + ... + a_{0}(x)= 0

where the coefficients *a*_{i}(*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.

An algebra function is in the form of,

a_{n}(x)y^{n} + a_{n-1}(x)y^{n-1} + ... + a_{0}(x) =
0

Where, a_{n}, a_{n-1}, a_{0} 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 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`