SLANT ASYMPTOTE WORKSHEET

About the topic "Slant Asymptote Worksheet"

Slant Asymptote Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on slant asymptote. 

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Slant Asymptote Worksheet - Problems

Problem 1 :

Find the equation of horizontal asymptote for the function given below. 

f(x)  =  1 / (x + 6)

Problem 2 :

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

f(x)  =  (x² + 2x - 3) / (x² - 5x + 6)

Problem 3 :

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

f(x)  =  (x² + 3x + 2) / (x - 2)

Slant Asymptote Worksheet - Solutions

Problem 1 :

Find the equation of horizontal asymptote for the function given below. 

f(x)  =  1 / (x + 6)

Solution :

Step 1 :

In the given rational function, the highest exponent of the numerator is 0 and the highest exponent of the denominator is 1. 

Step 2 :

Clearly highest exponent of the numerator is less than the highest exponent of the denominator. 

Hence, there is no slant asymptote.

Problem 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 highest exponent of the numerator is 2 and the highest exponent of the denominator is 2. 

Step 2 :

Clearly, the exponent of the numerator and the denominator are equal. 

Hence, there is no slant asymptote.

Problem 3 :

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

f(x)  =  (x² + 3x + 2) / (x - 2)

Solution :

Step 1 :

In the given rational function, the highest exponent of the numerator is 2 and the highest exponent of the denominator is 1.

Step 2 :

Clearly, the exponent of the numerator is greater than the exponent of the denominator by one. So, there is a slant asymptote. 

Step 3 :

To get the equation of the slant asymptote, we have to divide the numerator by the denominator using long division as given below.

Step 3 :

In the above long division, the quotient is (x + 5).

Hence, the equation of the slant asymptote is

y  =  x + 5

After having gone through the stuff given above, we hope that the students would have understood, "Slant Asymptote (Oblique)". 

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