Precalculus 2014

 PAGE: 138 SET: Exercises PROBLEM: 1

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 and .

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   and 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 , is a hozizantal asymptote of .

Domain, .

Vertical asymptotes, .

Horizantal asymptote, .

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