VERTICAL ASYMPTOTES WORKSHEET

Find the equation of vertical asymptote :

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

2. f(x) = (x2 + 2x - 3)/(x2 - 5x + 6)

3. f(x) = (2x - 3)/(x2 - 4)

4. f(x) = (2x - 3)/(x2 + 4)

1. Answer :

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

Step 1 :

In the given rational function, the denominator is

x + 6

Step 2 :

Equate the denominator to zero and solve for x.

x + 6 = 0

x = - 6

Step 3 :

The equation of the vertical asymptote is

x = - 6

2. Answer :

f(x) = (x2 + 2x - 3)/(x2 - 5x + 6)

Step 1 :

In the given rational function, the denominator is

x2 - 5x + 6

Step 2 :

Equate the denominator to zero and solve for x. 

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. Answer :

f(x) = (2x - 3)/(x2 - 4)

Step 1 :

In the given rational function, the denominator is

x2 - 4

Step 2 :

Equate the denominator to zero and solve for x.

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. Answer :

f(x) = (2x - 3)/(x2 + 4)

Step 1 :

In the given rational function, the denominator is

x2 + 4

Step 2 :

Equate the denominator to zero and solve for x.

x2 + 4 = 0

x2 = -4

x = ±√-4

x = ±2i

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

Step 3 :

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

So, there is no vertical asymptote.

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