Show all work. Simplify and clearly indicate all answers.

1. For the function − + + − 4 3 2 f(x) = 3x 4x x 6x 2
   a. State the degree of the polynomial.
   b. State the number of zeros the polynomial function will have.
   c. Use the Rational Zero Theorem to list all of the possible rational zeros
   d. Use trial and error to find two zeros of
   f x( )
   then write them in the table below.
   Zeros
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   Due: Upload to Lab 6 Canvas Dropbox by Sunday, April 11th by 11:59pm
   e. Use the quadratic formula to find the final two zeros.
   Zeros
   f. Rewrite
   f x( )
   as the product of linear factors.
2. Based on data from the U.S. Department of Agriculture, the average number of acres per farm x years after
   2000 can be approximated by the model below. (Round answers to 2 decimal places.)
   13x 2164
   2078x 94458 A(x)
   −

−

a. Use the model to estimate the average number of acres per farm in 2005.
b. Use the model to predict the average number of acres per farm in 2012.
c. Find and interpret the zero of the rational function. Does this result make sense within the
context of the problem? Answer in complete sentences using proper grammar and correct spelling.
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Due: Upload to Lab 6 Canvas Dropbox by Sunday, April 11th by 11:59pm

3. 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) =
   0.01t 3
   60(1 0.4t)
   +
   +
   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? Round to the nearest whole insect.
   c. Determine the horizontal asymptote of P(t) then describe what the horizontal asymptote means
   in the context of the problem. Use the value of the horizontal asymptote in the explanation.
   [Answer in a complete sentence using proper grammar and correct spelling.]
   d. Sketch the graph of P(t). Properly label both axes!
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   Due: Upload to Lab 6 Canvas Dropbox by Sunday, April 11th by 11:59pm
4. State the domain, vertical asymptote and slant asymptote of the function C(x) =
   x 6
   7x 8x 11 2
   −
   − +
   .
5. Draw a picture of something funny. [+5 points]