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Module 2                                                                                                                             37

   intercepts?

Rational Functions

1.    For each of the following rational functions:

      a.    Find the domain.

      b.    Find the vertical asymptote(s), if any.  If no vertical asymptote, write “No VA”.

c.

State whether the function has a horizontal asymptote, a slant asymptote or

neither;  then state the equation of the horizontal or slant asymptote, if any.

   A(x) =

   B(x) =

   C(x) =

   D(x) =

   E(x) =

2.  A rare species of insect was discovered in the rain forest.  In order to protect the species,  

    environmentalists declare the insect endangered and transplant the insects into a    

    protected area.  The population of the insect t months after being transplanted is     

    given by P(t).

   P(t) =

   a.  How many insects were discovered?  In other words, what was the population

        when t = 0?

   b.  What will the population be after 5 years?

   c.  Determine the horizontal asymptote of P(t).  What is the largest population that the

        protected area can sustain?

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