**Problem 1 :**

Find the equation of horizontal asymptote of the graph of

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

**Problem 2 :**

Find the equation of horizontal asymptote of the graph of

f(x) = (x^{2} + 2x - 3) / (x^{2} - 5x + 6)

**Problem 3 :**

Find the equation of horizontal asymptote of the graph of

f(x) = (x^{2} - 4) / (2x - 3)

**Problem 1 :**

Find the equation of horizontal asymptote of the graph of

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

**Solution : **

**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

**Problem 2 :**

Find the equation of horizontal asymptote of the graph of

f(x) = (x^{2} + 2x - 3) / (x^{2} - 5x + 6)

**Solution : **

**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 largest exponent of the numerator and the largest exponent of 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

**Problem 3 :**

Find the equation of horizontal asymptote of the graph of

f(x) = (x^{2} - 4) / (2x - 3)

**Solution : **

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

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

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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