HORIZONTAL ASYMPTOTES WORKSHEET

Find the equation of horizontal asymptote :

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

2. f(x) = (x² + 2x - 3)/(x² - 5x + 6)

3. f(x) = (x² - 4)/(2x - 3)

1. Answer :

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

Step 1 :

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

Step 2 :

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

So, equation of the horizontal asymptote is

y = 0 (or) x-axis

2. Answer :

f(x) = (x² + 2x - 3)/(x² - 5x + 6)

Step 1 :

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

Step 2 :

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

Step 3 :

Now, to get the equation of the horizontal asymptote, we have to divide the coefficients of largest exponent terms of the numerator and denominator.

So, equation of the horizontal asymptote is

y = 1/1

y = 1

3. Answer :

f(x) = (x² - 4)/(2x - 3)

Step 1 :

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

Step 2 :

Clearly, the largest exponent of the numerator is greater than the largest exponent of the denominator.

Step 3 :

Because the largest exponent of the numerator is greater than the largest exponent of the denominator, there is no horizontal asymptote.

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