$\"\"$

The function is $\"\"$ .

The domain of the function is set of all values at which the function is continuous.

The denominator should not be equal to $\"\"$ .

$\"\"$ $\"\"$

Therefore the function is undefined at the real zero of the denominator $\"\"$ .

The real zeros of $\"\"$ is $\"\"$ .

Thus, the function is continuous for all real numbers except $\"\"$ .

Therefore Domain, $\"\"$ .

$\"\"$

Check for vertical asymptotes :

Determine whether $\"\"$ is a point of infinite discontinuity.

Find the limit as $\"\"$ approaches $\"\"$ from the left and the right.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Because $\"\"$ is a vertical asymptote of $\"\"$ .

$\"\"$

Determine whether $\"\"$ is a point of infinite discontinuity.

Find the limit as $\"\"$ approaches $\"\"$ from the left and the right.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Because $\"\"$ and $\"\"$ is a vertical asymptote of $\"\"$ .

$\"\"$

Check for horizantal asymptotes :

Draw the table to determine the end behaviour of $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

From the table: $\"\"$ and $\"\"$ .

Therefore there is no horizantal asymptote for the above function.

$\"\"$

Domain, $\"\"$ .

Vertical asymptotes, $\"\"$ .

No horizantal asymptote.