# GRAPHING RATIONAL FUNCTIONS WITH HOLES

## About the topic "Graphing rational functions with holes"

"Graphing rational functions with holes" is a much needed stuff for almost all the students who study math in high schools.

Even though students can get this stuff on internet, they do not understand exactly what has been explained.

To make the students to understand the stuff "How to graph rational functions with hole", we have given step by step explanation.

## Rational function - Example Before learning "Graphing rational functions with hole", first you have to be knowing the following stuff.

1. Vertical Asymptote

2. Horizontal Asymptote

3. Slant Asymptote

4. Hole

To know more about the above mentioned stuff, please click the topics given above.

If you had already learned the above mentioned stuff, then you are ready to learn the stuff, "How to graph rational functions with hole".

Now let us take an example and understand "How to graph rational functions with holes".

Example :

Graph the rational function given below. Solution :

Step 1:

First, we have to find hole, if any.

To find hole of the rational function, we have to see whether there is any common factor found at both numerator and denominator.

So, let us factor both numerator and denominator.

y = [(x-2)(x+1)] / (x-2)

In our problem, clearly there is a common factor (x-2) found at both numerator and  denominator. So, there is a hole.

Step 2:

Now, we have to cross out the common factor (x-2) at both numerator and denominator as given below. Step 3:

Now we have to make the common factor (x-2)  equal to zero.

When we do so, we get

x - 2 = 0 ===>  x  =  2

So, the hole is at  x = 2

Step 4:

After having crossed out the common factor (x-2), the function is simplified to f(x) = x+1   or   y = x+1.

Step 5:

Now, if we plug x = 2 in y = x+1, we get y = 3.

Hence, the hole appears on the graph at (2 , 3)

Step 6:

In y = x + 1, now we have to plug some random values for "x" and find the corresponding values  of "y" as given in the table below. ## Graph of the given rational function  