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# Graphing Simple Rational Functions

TopRational function can be defined as Ratio of two Polynomials. Numerator and denominator values are present in case of Rational Function, and value present in denominator of rational function cannot be equals to zero. In other words rational function can be defined as ratio of two polynomials. For example: u2 + 9 / u + 5, as it is the ratio of two polynomials. Now we will discuss Graphing of simple rational Functions.
Suppose we have a rational function f (u) = u2 - 4 / u2 – 4u, then we can plot graph of rational function as shown below.
Solution: - To plot graph of this function we need to follow some steps.
Step 1: First of all check whether the function is rational function or not. According to the definition of rational functions it is ratio of two polynomials. So rational function is:
=> f (u) = u2 - 4 / u2 – 4u,
Here in this above function we cannot put value of denominator as zero because when we put value of denominator as zero then whole function changes to infinity. y – intercept will not be present in graph.

Step 2: Put numerator value equals to zero to obtain the value of 'x'.
So we can write numerator value as:a
=> u2 – 4 = 0, so here we get two values of 'u' that is u = + 2.
Above function can also be written as:
= u2 – 4 = u (u – 4) = 0, so here we get value of 'u' as 0 and 4.

Step 3: Now put different values of 'u' to get more values.
When we put values of 'u' as 1, 3 and 5 then we get other values 1, -5 / 3 and 21 / 5 respectively. Using these coordinates value we can plot graph of rational function. Graph of rational function is shown below:

This is how we plot simple rational function graph.