A function is a connection between an independent variable $(X)$ and a dependent variable $(Y)$. The relationship between the variables is called a "correspondence rule".

An algebraic representation of a function is actually a description of the relationship between the dependent variable$(Y)$ and the independent variable$(X)$ by means of an equation.

The following is the typical structure of a graphical representation:

In some related articles, it had been mentioned that a function can be represented in different ways, verbally, algebraically, with tables and graphically. In the case of how to represent a function algebraically, in a few words we can say that it will be represented in an equation, which will indicate the rule of correspondence between the dependent variable $Y$ and the independent variable. $X$

What is the algebraic representation of a linear function?

The representation of a linear function is the one where we are going to visualize an equation where it represents a straight line, that is to say the independent variable $X$ this with an exponent one, that is to say, of first degree.

Examples

Some algebraic representations of a linear function are the following:

$y=x+4$

$y=-x+1$

$y=x-5$

$y=-x-1$

We can observe that the variable $X$ has as exponent one, and if we graph these functions we will always get a straight line, so they represent a linear function.

How is the algebraic representation of a quadratic function?

A quadratic function can be seen as an equation where the variable $X$ will have the exponent $2$, which will represent a parabola if it is graphed. Some examples are the following:

$y=x^2+4$

$y=x^2-3$

$y=-x^2+5$

How to get the algebraic representation of a table?

A function can be represented verbally, algebraically, in a table of values and graphically, therefore, we can go from one representation to another, in this case we are going to study how to go from a table to an algebraic representation, for such a case let's see the following example:

Example

Assignment

From the following table find its algebraic representation.

Solution:

From the previous table we are going to take any two points, in order to get its slope: