We will be able to find vertical asymptotes of a function, only if it is a rational function.

That is, the function has to be in the form of

f(x) = g(x) / h(x)

**Rational Function - Example : **

**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

**Example 1 : **

Find the equation of vertical asymptote of the graph of

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

**Example 2 : **

Find the equation of vertical asymptote of the graph of

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

**Solution : **

**Step 1 : **

In the given rational function, the denominator is

x^{2} - 5x + 6

**Step 2 :**

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

That is,

x^{2} - 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

**Example 3 :**

Find the equation of vertical asymptote of the graph of

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

**Solution : **

**Step 1 : **

In the given rational function, the denominator is

x^{2} - 4

**Step 2 :**

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

That is,

x^{2} - 4 = 0

x^{2} - 2^{2} = 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

**Example 4 :**

Find the equation of vertical asymptote of the graph of

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

**Solution : **

**Step 1 : **

In the given rational function, the denominator is

x^{2} + 4

**Step 2 :**

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

That is,

x^{2} + 4 = 0

x^{2} = - 4

x = ± √-4

x = ± 2i

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

**Step 3 :**

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

So, there is no vertical asymptote.

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