COLLEGE ALGEBRA
MATH 110
Southwestern   
Adventist University 
 
     Distance Education Lawrence E. Turner, Jr., Ph.D.  


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SAMPLE TEST QUESTIONS

1999

(Barnett, Ziegler, and Byleen)


Chapter 3      Graphs and Functions

3.1     basic tools: circles

30.     What is the distance between the following sets of points:
  1. (1,2) and (-3,4)
    (5)
  2. (-3,4) and (4,-3)
    (5)
  3. (-3,-2) and (-3,4)
    (5)

31.     Does the triangle defined by the three points (1,2), (5,1), and (6,3) form a right triangle? Explain.
(10)


32.     What is the equation of a circle with a center at (3,4) and a radius of 3?
(5)


33.     For the circle given by:

  1. what is the location of the center?
    (3)
  2. what is its radius?
    (2)

34.     For the circle given by:
  1. what is the location of the center?
    (5)
  2. What is its radius?
    (5)


3.2     straight lines

35.     What are the slopes and y-intercepts of the following lines?
  1.  
    (5)
  2.  
    (5)
  3.  
    (5)

36.     Write an equation for the line that:
  1. has a slope of -1 and a y-intercept of 2
    (5)
  2. has a slope of 1/2 and a y-intercept of -1
    (5)
  3. passes through the two points (-1,6) and (2,-2)
    (5)
  4. passes through the two points (1,4) and (-6,-2)
    (5)
  5. through the point (1,-3) and parallel to the line:
    (5)
  6. through the point (1,-3) and perpendicular to the line:
    (5)


3.3     functions

37.     Do the following relations define a function? Explain
  1.  
    (5)
    {(1,2),(1,3),(2,4),(3,6)}
  2.  
    (5)
    {(1,2),(2,3),(4,3),(6,4)}
  3.  
    (5)
  4.  
    (5)
  5.  
    (5)
  6.  
    (5)

38.     What is the natural domain of the following?
  1.  
    (5)
  2.  
    (5)
  3.  
    (5)
  4.  
    (5)
  5.  
    (5)

39.     What is the range of the following--assume a natural domain?
  1.  
    (5)
  2.  
    (5)
  3.  
    (5)


3.4     graphing functions

40.     On what part of the domain is the following function increasing? decreasing?

(5)
41.     Is the function f(x) = 3 a linear function? Why or why not?
(5)


42.     For the following quadratic functions, find the axis of symmetry, the vertex, the y-intercept, and the x-intercepts, and sketch the graph of the function.
  1.  
    (15)
  2.  
    (15)


3.5     combining functions

43.     For the functions:

  1. what are the domains of f(x) and g(x)?
    (4)
  2. compute f+g and its domain
    (4)
  3. compute f-g and its domain
    (4)
  4. compute fg and its domain
    (4)
  5. compute f/g and its domain
    (4)
  6. compute fog and its domain
    (8)
  7. compute gof and its domain
    (8)


44.     For the functions:
  1. what are the domains of f(x) and g(x)?
    (4)
  2. compute f+g and its domain
    (4)
  3. compute f-g and its domain
    (4)
  4. compute fg and its domain
    (4)
  5. compute f/g and its domain
    (4)
  6. compute fog and its domain
    (8)
  7. compute gof and its domain
    (8)

45.     What is the effect on the graph of f(x) when you
  1. use f(x+2)
    (5)
  2. use f(x)+5
    (5)
  3. use -f(x)
    (5)
  4. use 2f(x)
    (5)


3.6     inverse functions

46.     Are the following functions one-to-one? Explain
  1.  
    (5)
  2.  
    (5)
  3.  
    (5)
  4.  
    (5)


47.     Find the inverse function for
  1.  
    (10)
  2.  
    (10)
  3.  
    (10)

48.     What is the relationship between the graph of f(x) and f(x)-1?
(5)


49.     What is f(x)of(x)-1?
(5)
  
© 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 by Lawrence Turner