#graphing rational functions

[math-journal2]

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[math-journal2]

Rational Functions

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Edit:

D > N —> y = 0

D = N —> y= a (sub n) / b (sub n)

D < N —> y = mx + b

[mathematicalanalysis-blog-blog]

Graphing Rational Functions

Previously we have discussed about how to solve equations with fractions and In today's session we are going to discuss about Rational numbers, They are those numbers which represent the number ‘x’ and ‘y’ in the form x / y.  In the given form x can be defined as value of numerator and y can be defined as value of denominator. When we use the concept of rational numbers with the arithmetical function then concepts are used by rational function. In a mathematical definition rational function can be described by in the given form:

                      f ( e ) =  a ( e ) / b ( e )

In the above form of rational function, f (e) is a function of ‘e’ and ‘a (e)’ and ‘b(e)’ are the polynomial functions. In the function value domain of function f is the set of all real numbers. One thing to always remember is the value of denominator in function of e, it means value of b(e) is not equal to zero. If in the rational function’s denominator does not contain a variable value than that function is not considered as rational function. Example: suppose f (y) =  y + 4 / 3, here the value of denominator is not a variable then we can say that this is not a rational function. After obtaining various value of function f (e), we can plot this value on graph. These concepts are known as Graphing Rational Functions.

Now in the following example we show you how to solve the rational function:

Example: Solve the given rational function:

                                    f (e) = e + 2 / e – 4

Solution: In the above function value we need to put the value of e in that manner which not makes the denominator zero.

           So, excepting value 4 we can put any real number into the function or denominator. So by putting x = 5 the f (e) will be,

                      f (5) = 5 + 2 / 5 – 4

                      f (5) = 3

In the same manner by putting value another value we can obtain another function’s value.

In the next session we are going to discuss conic section and You can visit our website for getting information about how to factor polynomials and Political Science Tamilnadu Board Sample Paper.

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[mathematicalanalysis-blog-blog]

Rational Function

Previously we have discussed about real numbers definition and In today's session we are going to discuss about Rational Function, Ratio of two polynomial functions is known as the rational function. A rational function F(a) can be given as-

F (a) = p (a) / q (a), where ‘a’ is the variable on which function depends.

In the above function ‘p’ and ‘q’ are two polynomial functions and it should be noted that value of q ( a ) should never be zero. Here the function ‘f’ is defined as the domain of sets of all points ‘a’ for that, denominator q (a) will never be zero.

Keep in mind that every polynomial function is a rational function if q( a ) =1. Suppose we have  a function written as f ( a ) = cos ( a ), then it is not a rational function .

 So a rational function or a rational expression is defined in the form p (a) / q (a) here ‘a’ is not a variable but it is an indeterminate in the abstract algebra. Same rules of fraction also apply on the rational equation .We can understand the rational expression by rational function examples.

Some examples for defining the rational expression are as follows:

Here is a rational function f (a) = (a 3 – 2 a) / 2 ( a 2 – 5 ) but it is clear that for value a2 = 5, function is not rational.

Another example f ( a ) = (a 2 + 2) / (x 2 + 1) is a rational function for all real numbers but keep in mind that it is not a rational function for complex numbers .

In the next session we are going to discuss about Limits of sequence and function and You can visit our website for getting information about math tutor online and icse class 10 syllabus.