Mississippi Mu Alpha Theta
Precalculus Written Exam 2009
1. Which, if any, of the following statements are true.
I. Functions with x-axis symmetry are even functions.
II. Functions with origin symmetry are odd functions.
III. Functions cannot have x-axis symmetry.
IV. Functions cannot have origin symmetry.
A. I, II
B. I, IV
C. II, III
D. II only
E. None of these
2. Find all of the possible rational zeros of the function: f ( x)  6  27 x  3x3  4 x 2
A. 1, 3,  16 ,  12
C. 1, 2, 3, 6,  13 ,  23
B. 1, 2, 6,  13
D. 1, 2, 3,  16 ,  13 ,  12 ,  23
E. None of these
3. Determine the end behavior of the following polynomial: f ( x)  1  x3  x5 .
A.
C.
As x  , f(x)  
B.
As x  , f(x)  
As x  , f(x)  
D.
As x  , f(x)  
As x  , f(x)  
As x  , f(x)  
As x  , f(x)  
As x  , f(x)  
E. None of these
4. Find the minimum point on the graph of f ( x)  x 2  4 x  14
A. (2,10)
B. (-2,18)
C. (-2,26)
D. (2,18)
E. None of these
5. Write as a product of linear factors: f ( x)  x 4  3x 2  28
A. ( x2  4)( x2  7)
B. ( x  2i )( x  2i )( x  7)( x  7)
C. ( x  2i )( x  2i )( x  7)( x  7)
E. None of these
D. ( x  2i )( x  2i )( x  7)( x  7)
6. Find the domain of the function: f ( x) 
x2
x2  4
A. (, 4)  (4, ) B. (, 2)  (2, 2)  (2, )
D. (, 2)  (2, ) E. None of these
C. ( 2, 2)
Mississippi Mu Alpha Theta
Precalculus Written Exam 2009
7. Find the holes and vertical asymptotes (V.A.s) for the given function: f ( x) 
x2  5x  6
x3  4 x
A. V.A. at x = 0, x = 2, and x = -2
B. V.A. at x = 0 and x = 2; Hole at (-2, 0)
C. V.A. at x = 0 and x = -2; Hole at (2, -1/8)
D. V.A. at x = 1 and x = -2; Hole at (2, 0)
E. None of these
8. Determine the end behavior of the given function: f ( x) 
A.
C.
As x  , f(x)  
As x  , f(x)  
As x  , f(x)  1
As x  , f(x)  1
B.
D.
2x 1
3x  5
As x  , f(x)  
As x  , f(x)  
As x  , f(x)  2 3
As x  , f(x)  2 3
E. None of these
9. Describe the transformation of the graph of f ( x)  x to the graph of g ( x)  2  x  5 .
A. Vertical shift 5 units up; horizontal shift 2 units left
B. Vertical shift 5 units down; horizontal shift 2 units down
C. Vertical shift 2 units down; horizontal shift 5 units to the right
D. Vertical shift 2 units up; horizontal shift 5 units to the left
E. None of these
10. Describe the transformation(s) needed to obtain the graph of
g ( x)   x  6 from the graph of the figure on the right.
A. Reflection across the x-axis; Vertical shift 6 units up
B. Reflection across the y-axis; Vertical shift 6 units down
C. Reflection across the y-axis; Vertical shift 1 unit up
D. Reflection across the x-axis; Vertical shift 1 unit down
E. None of these
Mississippi Mu Alpha Theta
Precalculus Written Exam 2009
11. Solve for x: 2(32 x )  6  168
A. 2
B. 4
C. log3 78
D. log6 78
E. None of these
D. 2,  73
E. None of these
12. Solve for x: log10 (3x  1)  log10 ( x  2)  1
A.
8
3
B. 3,  83
C.3
13. Determine the open intervals in which the function is increasing, decreasing, and constant.
A. Increasing on ( 4, 4)
B. Increasing on (4, 2)  (1, 2)  (2, 4)
Decreasing on (2, 1)
C. Increasing on (4,1)  (2, 4)
Decreasing on (1, 0)  (1, 2)
D. Increasing on (2, 1)
Decreasing on (1, 0)  (1, 2)
Constant (4, 2)  (0,1)  (2, 4)
E. None of these
14. Find a fourth degree polynomial with real coefficients that has zeros: 2,3, 2 i
A. x 4  5 x 2  6
C. x 4  5 x3  4 x 2  10 x  12
E. None of these
B. x 4  5 x3  8 x 2  10 x  12
D. x3  3 x 2  4 x  12
15. Find two functions f ( x) and g ( x ) such that ( f g )( x)  h( x) where h( x) 
2
A. f ( x)  , g ( x)  x 2  4
x
C. f ( x) 
2
, g ( x)  x  4
x2
B. f ( x)  x 2  4, g ( x) 
D. f ( x)  x  4, g ( x) 
2
x 4
2
2
x
2
x2
E. None of these
16. Find the sum of the integers in the interval [50, 200].
A. 18875
B. 250
C. 26425
D. 37500
E. None of these
Mississippi Mu Alpha Theta
Precalculus Written Exam 2009

17. Find the sum of the infinite geometric series, if it exists:
 6(0.7)
n 1
.
n 1
A. 2
B. 14
C. -2
D. 20
E. The sum does not exist
18. Solve for x: e2 x  3e x  2  0 .
A. x  0, x  ln 2
C. x  ln 2
B. x  0
D. x  0, x  ln(2)
E. None of these
19. Find the sum of the numerators for the partial fraction decomposition of
A. 2
B. 1
C. -2
D. -1
x7
.
x  x6
2
E. None of these
20. The level of sound  , in decibels, with an intensity of I is   10 log10
I
, where I 0 is an
I0
intensity of 10 12 watts per square meter, corresponding roughly to the faintest sound that can be
heard by the human ear. Find the level of sound for an air hammer with
intensity I  102.5 watt per m2 .
A. 145 decibels
D. 95 decibels
B. 85 decibels
E. None of these
C. 105 decibels