Precalculus Practice Exam

Part 1	Test 3	Time: 1 hour

1. Solve the following equation for x:

   

   Answer: , and .

2. Solve the following inequality for x:

   

   Answer: The set of values x<5.

3. Given the two points (-1,8) and (3,-4), find the following:
   • The distance between the two points.

     Answer: The distance is .

   • The midpoint of the two points.

     Answer: The midpoint is (1,2).
     

   • An equation of the line containing the two points.

     Answer: An equation of the line is y=-3x+5.
     

   • An equation of the circle whose diameter is the line between the two points.

     Answer: The circle is the locus of the points described by

     
     

4. Concerning the following graph of f(x),
   
   • Approximate the interval(s) where the function is increasing.

     
     Answer: The function is always increasing, thus, the increasing interval is .

   • Approximate the interval(s) where the function is decreasing.

     
     Answer: The function is never decreasing.

   • Approximate the relative maximum value of the function.

     
     Answer: Since the function is always increasing, there is no maximum value.

   • Approximate the relative minimum value of the function.

     
     Answer: There is no minimum value of the function.

5. Concerning the graph of f(x) in Problem 4, sketch the following:
   • -f(x).
     Answer:
     

   • f(x)+3.
     Answer:
     

   • f(x-4)-6.
     Answer:
     

6. Given the functions and ,
   • Find (f+g)(x).

     Answer:

     

   • Find .

     Answer:

     

   • Find .

     Answer: f(g(x))=|x|-3.

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Tue Jun 24 15:37:09 MDT 1997

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