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| 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.
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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.
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Because 
and 
is a vertical asymptote of 
.
Check for horizantal asymptotes :
Draw the table to determine the end behaviour of 
.
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From the table 
and 
,
is a hozizantal asymptote of .
Domain, .
Vertical asymptotes, 
.
Horizantal asymptote, 
.
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