Algebraic Function

A function is a fundamental topic of mathematics. It gives rise to several fields of mathematics with different approaches and applications. Algebraic functions are one of the most important functions of mathematics that have several topics like roots, solutions, and polynomial equations. These functions can be fun to do alphanumeric operations with interesting tricks and questions in the right way. This article will provide a detailed guide on algebraic functions and will briefly define the concept of visual function and function graphs. Read more and follow.

What is a function in math?

There can be several definitions concerning different applications as an answer to “what is a function in math?”. While in general mathematics, a function can be referred to as a law expression or fuel signifying a relationship between an independent variable and a dependent variable. Functions are the base of physical relationships, eventually making them essential for science. Peter Dirichlet, a German mathematician, defined a function in modern definition in 1837.  A function pertains to the relationship that can be symbolized in the form 

y=f(x) 

This symbolization of function is pronounced as F is a function of x, and for every value of x, there exists a unique and distinct value of y. Concerning the set theory, a modified definition states that a function is a relationship between an element x to another element f(x) in another set.

There are different types of functions in mathematics like:

• One to One function

• Many to One function

• Onto function 

• Polynomial function

• Identity function

• Trigonometric function

• Algebraic function

• Modulus function

The list of mathematical functions doesn’t end here. There are hundreds of functions as we dive deeper into modern mathematics. 

All you need to know about the algebraic function

A combination of algebraic operations in a function defines an algebraic function. Furthermore, algebraic operations include several operations like exponentiation, addition, multiplication, subtraction, and division.

To help you understand better here are a few examples of algebraic functions:

• f(x)= x3-6x+8

• h(x)= √x

• g(x)= (7x+8)/(4x+5)

• f(x)= X7

The highest exponentiation of variables in an equation of function defines the function’s degree, which gives the notation. There are several notations like quadratic, linear, cubic, and polynomial functions. An algebraic function only includes addition, subtraction, multiplication, division, exponential, and roots. 

Introduction to Algebraic function graph

Every algebraic function has a certain graph with variable size and form to provide distinctness in the algebraic function graph. Here is a step by step guide to plot a graph of any function of the form

 y = f(x)

1. Put y=0 and calculate the x coordinates 

2. Put x=0 and calculate the y coordinates

3. Find and plot all the asymptotes

4. Calculate the inflection points and critical points

5. Now for the final function graph, you need to plot all these points and form the graphing function of that particular function.

Non-Algebraic Functions

There are several other non-algebraic functions like logarithmic functions, exponential functions, trigonometric functions, and several other functions. Let’s have a look at a few examples of non-algebraic functions to make the difference clear:

f(x) = sin ( 5x+2)

g(x) = log x

h(x) = 6x

Now that you have understood the difference between algebraic and non-algebraic functions, it should be quite easy to identify algebraic functions. Let us understand the different types of Algebraic functions.

Polynomial Functions

The polynomial functions refer to functions that include the domain of real numbers, and the range is defined by the y-values covered in the Function graph. Different functions depend upon the degree; we will discuss a few of them with one example of each type.

• Linear Function

f(x) = 5x+8

• Quadratic Function

f(x) = X2+8x+6

• Cubic Function

f(x) = X3+6x2-4x-5

• Biquadratic Function

f(x) = X4+6x3-5x2+2x-6

Power Functions

The general form of power functions is f(x) = k xa

Where,

k and a belong to the set of real numbers. A few examples of power functions are given below:

• f(x) = X4

• f(x) = x-2

• f(x) = √x-3 

• f(x)= (x-3)⅓

Rational Functions

The rational function refers to a function that involves variables in the numerator and denominator part of a fraction.  These fractions have a general form of f(x) = p(x)/q(x), where q(x) and p(x) are polynomials in x. A few examples of Rational Functions are:

• f(x) = (x-2)/ (3x2+4x-3)

• f(x) = (5x+7)/(3x3+5x+8)

Conclusion

Mathematics has several functions that work and functions as a basic requirement to solve various physical and mathematical problems. An algebraic function is also a well-known algebraic function, and it encapsulates a collection of functions like polynomials, power, and rational functions. This article provides a brief guide on drawing and deducing a function graph from a given function and detailed information with a few examples of different types of algebraic functions.