HOW TO FIND VERTICAL ASYMPTOTE OF A FUNCTION

About the topic "How to find vertical asymptote of a function"

"How to find vertical asymptote of a function ?" is the question having had by the students who are studying math in school final. Even though it is taught by the teachers in school and university, students do not understand this clearly. Often students have this question on vertical asymptotes. 

On this page of our website, we have given step by step explanation and examples to make the students to clearly understand how to find vertical asymptote of a function.  

And we will be able to find vertical asymptote of a function, only if it is a rational function.

That is, the function has to be in the form of f(x) = P/Q

Example : Rational Function

Steps involved in finding vertical asymptotes

Step 1 :

Let f(x) be the given rational function.Make the denominator equal to zero.

Step 2 :

When we make the denominator equal to zero, suppose we get  x = a and  x  =  b. 

Step 3 :

The equations of the vertical asymptotes are 

x = a and x = b.

Examples:

1. Find the equation of vertical asymptote for the function given below. 

f(x) = 1/(x+6)

Solution :

Step 1:

In the given rational function, the denominator is (x+6).

Step 2 :

Now, we have to make the denominator equal to zero.

That is,                                    x+6 = 0

                                                    x = -6

Step 3 :

The equation of the vertical asymptote is 

x = -6

2. Find the equation of vertical asymptote for the function given below. 


f(x) = (x²+2x-3)/(x²-5x+6)

Solution :

Step 1:

In the given rational function, the denominator is x²-5x+6.

Step 2 :

Now, we have to make the denominator equal to zero.

That is,                                    x²-5x+6 = 0

(x-2)(x-3) = 0

x-2 = 0 or x-3 = 0

x = 2 or x = 3

Step 3 :

The equations of two vertical asymptotes are

x = 2 and x = 3

3. Find the equation of vertical asymptote for the function given below. 

f(x) = (2x-3)/(x² -4)

Solution :

Step 1:

In the given rational function, the denominator is (x² -4).

Step 2 :

Now, we have to make the denominator equal to zero.

That is,                                    x² -4 = 0

x²  - 2² = 0

(x+2)(x-2) = 0

x = -2 or x = 2

Step 3 :

The equations of two vertical asymptotes are

x = -2 and x = 2


4. Find the equation of vertical asymptote for the function given below. 

f(x) = (2x-3)/(x² +4)

Solution :

Step 1:

In the given rational function, the denominator is (x² +4).

Step 2 :

Now, we have to make the denominator equal to zero.

That is,                                    x² +4 = 0

x² = -4

x =±√-4 

x = 2i or x = -2i (Imaginary)

Step 3 :

When we make the denominator equal to zero, we don't get real values for "x".

Hence, there is no vertical asymptote.




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