Precalculus Practice Exam

Part 3	Test 2	Time: 1 hour

1. Let .
   • Sketch the graph of identifying any intercepts and asymptotes.
     

     Answer:
     

     

     The graph has no y-intercept; its only x-intercept is at . The graph has no asymptotes, but some people consider x=2 a vertical asymptote.

   • Give the domain and range of .
     

     Answer: The domain of the function are all numbers x>2; the range of the function consists of all real numbers.

2. Solve for x algebraically:
   • 
     

     Answer: or

   • 
     

     Answer: x=2.

3. Compress the expression into one simplified logarithm.
   

   Answer:

   Give the domain of the original expression.
   

   Answer: The domain is x>1

4. In 1967, Dr. Christian Barnard of South Africa stunned the world by performing the world's first heart transplant. There was one transplant in 1967. In 1987, there were 1,418 such transplants.
   • Find the exponential growth function that fits this data.
     

     Answer:

   • Use the function to predict the number of heart transplants in 1998.
     

     Answer: There will be approx. 76,753 in the year 1998.

5. Solve the system algebraically:

   

   
   

   Answer:

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Wed Jun 18 15:14:34 MDT 1997

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