College Algebra
Final Examination—FHSU Math & C.S. Department
Form G Name ____________________________
Multiple Choice:
Mark through (horizontally) the space on the answer card corresponding to the best answer for each
problem.
1. Solve the equation by factoring: 2 9 18 0x x
[A] 6, 3 [B] 6, 3 [C] 6, 3 [D] 6, 3
2. Write the product in the standard form a + bi: (2 6 )(2 9 )i i
[A] 58 6i [B] 50 30i [C] 58 6i [D] 2
54 6 4i i
3. Find the real solutions of the equation 14 21 2 .x x
[A] 5 [B] 3 [C] 4 [D] 5
4. Solve the inequality 3 7 2 4x x . Express your answer using interval notation.
[A] 11, [B] [3, ) [C] 3, [D] ( , 3]
5. Solve the equation 3 3 18.x
[A] 3, 9 [B] 3 [C] 9, 3 [D] no solution
6. Solve the inequality 5 1 5x . Express your answer using interval notation.
[A] 645 5, or , [B] 64
5 5 ,
[C] 645 5, [D] 64
5 5 , or ,
7. A bank loaned $68,000, part of it at a rate of 15% per year and the rest at a rate of 5% per year. If the
interest received was $6600, how much was loaned at 15%?
[A] $36, 000 [B] $33, 000 [C] $32, 000 [D] $35, 000
8. Find the distance between the points 1 2(2, 2) and ( 10, 3).PP
[A] 14 [B] 26 [C] 169 [D] 13
9. List the intercepts for the graph of the equation 2
16 0.x y
[A] ( 4, 0), (0,16), (4, 0) [B] (4, 0), (0,16), (0, 16)
[C] (0, 4), (16, 0), (0, 4) [D] ( 4, 0), (0, 16), (4, 0)
2
10. Find the slope-intercept form of the equation of the line that is parallel with the given properties:
( 2, 3); and 9 20y x
[A] 9 15y x [B] 9 20y x [C] 1
20 9
y x [D] 1
20 9
y x
11. Write the standard from of the equation of the circle with radius 5 and center (1, 4) .
[A] 2 2
4 1 25x y [B] 2 2
1 4 5x y
[C] 2 2
4 1 25x y [D] 2 2
1 4 5x y
12. Write a general formula to describe the variation.
The illumination I produced on a surface by a source of light varies directly as the candlepower c of
the source and inversely as the square of the distance d between the source and the surface.
[A] 2
I kcd [B] 2
2
kc I
d [C]
2
kc I
d [D]
2 kd
I c
13. For the given functions ( ) 6 3 and ( ) 7 9f x x g x x , determine ( )( ).f g x
[A] 2
( )( ) 4 27f g x x [B] 2
( )( ) 13 33 6f g x x x
[C] 2
( )( ) 42 33 27f g x x x [D] 2
( )( ) 42 12 27f g x x x
14. The graph of a function f is given. For what values of x is
( ) 0f x ?
[A] 15,17.5
[B] 15,17.5, 25
[C] 15
[D] 25, 15,17.5, 25
15. Determine whether the function 3 2
( ) 4 9f x x is even, odd, neither, or both.
[A] Even [B] Odd [C] Neither [D] Both
16. Determine the average rate of change for the function 2
( ) 2f x x x from 5 to 9 using ( ) ( )
. f b f a
b a
[A] 16 [B] 64
9 [C] 11 [D]
99
4
-25 -15 -5 5 15 25
-15
5
15
-5
-25
3
17. The graph of a function f is given. Determine the values
of x at which f has a local minimum.
[A] 3.3, 2.5
[B] 2.5, 5
[C] 3.3, 5
[D] 2.5, 2.2
18. Determine the function that is graphed after the following transformations are applied to the graph of
y x . The graph is shifted right 4 units, stretched by a factor of 3, and shifted vertically down 2
units.
[A] 3 4 2y x [B] 3 4 2y x [C] 3 4 2y x [D] 3 4 2y x
19. Find and simplify the difference quotient, ( ) ( )
, 0 f x h f x
h h
, for the function ( ) 4 5.f x x
[A] 4 [B] 0 [C] 10
4 h
[D] 8( 5)
4 x
h
20. Suppose that 2
( ) 2 3 and ( ) 2 3f x x x g x x , solve ( ) ( )f x g x
[A] 1
, 3 2
[B] 1
, 3 2
[C] 0, 3 [D] 0, 3
21. Linda needs to have her car towed. Little Town Auto charges a flat fee of $80 plus $2 per mile towed.
Write a function expressing Linda’s towing cost, c , in terms of miles towed, x .
[A] ( ) 2c x x [B] ( ) 2 80c x x [C] ( ) 80 2c x x [D] ( ) 2 80c x x
22. Determine the x-intervals where the function graphed at
the right is decreasing.
[A] decreasing on (5, 3.3) and (3.9, 2.5)
[B] decreasing on ( , 8), ( 2.5, 2.2), and (5, )
[C] decreasing on ( 8, 2.5) and (2.2,5)
[D] decreasing on ( 5,0) and (4,5)
4
23. Identify the vertex of the graph of the function 2
( ) 6 5.f x x x
[A] ( 3, 4) [B] (3, 4) [C] (3, 4) [D] ( 3, 4)
24. Determine the quadratic function whose graph is given.
[A] 2
( ) ( 2) 1f x x
[B] 2
( ) ( 1) 2f x x
[C] 2
( ) ( 1) 2f x x
[D] 2
( ) ( 2) 1f x x
25. The number of mosquitos ( )M x , in millions, in a certain area depends on the June rainfall x , in
inches: 2
( ) 10M x x x . What rainfall produces the maximum number of mosquitos?
[A] 0 inches [B] 5 inches [C] 100 inches [D] 10 inches
26. Solve the inequality 2
3 2x x .
[A] ,1 or 2, [B] ,1 [C] 2, [D] 1, 2
27. Form a polynomial of degree 3 whose zeros are –5 with multiplicity 2 and 4 with multiplicity 1.
[A] ( ) ( 5)( 5)( 4)P x x x x [B] ( ) ( 5)( 5)( 4)P x x x x
[C] ( ) ( 5)( 2)( 4)P x x x x [D] ( ) ( 5)( 4)( 4)P x x x x
28. What are the x- and y-intercepts of the function 2
( ) ( 2) 6 1f x x x x ?
[A] -intercepts are ( 6, 0), (1, 0), (2, 0)
-intercept is (0,12)
x
y
[B]
-intercepts are ( 2, 0), (1, 0), (6, 0)
-intercept is (0, 12)
x
y
[C] -intercepts are ( 6, 0), (1, 0), (2, 0)
-intercept is (0, 12)
x
y
[D]
-intercepts are ( 2, 0), (1, 0), (6, 0)
-intercept is (0,12)
x
y
5
29. What is the domain of the rational function 2
2 ( )
16
x f x
x x
?
[A] | 0, 16x x x [B] | 4, 4x x x
[C] | 4, 4, 2x x x x [D] | 0, 16x x x
30. Write the equation of all vertical asymptotes of the rational function 2
2 ( )
16
x f x
x x
.
[A] 16x [B] 0, 16x x [C] 4, 4x x [D] 2x
31. Write the equation of the horizontal asymptote of the rational function 2
2 ( )
16
x f x
x x
.
[A] 2y [B] 0y [C] 1
8 y [D] 16y
32. Which of the following displays a graph of a polynomial that has ( 3)x as a factor with odd
multiplicity?
[A] [B]
[C] [D]
6
33. Which of the following best represents the left and right behaviors of the given graph:
[A] ( ) as
( ) as
f x x
f x x
[B] ( ) as
( ) as
f x x
f x x
[C] ( ) as
( ) as
f x x
f x x
[D] ( ) as
( ) as
f x x
f x x
34. The function 2 1
( ) 3
x f x
is one-to-one. Find its inverse.
[A] 3 1
2
x [B]
3
2 1x [C]
3
2 1x
[D]
2 1
3
x
35. Solve the exponential equation 7 3 1
4 2
x .
[A] 1 [B] 3 [C] 3 [D] 1
2
36. Using technology, approximate the value of 5
log 20 accurate to four decimal places.
[A] 2.3412 [B] 1.8614 [C] 0.5372 [D] 1.2523
37. Through the properties of logarithms, write 4 3
8 log
x
x
as the sum and/or difference of logarithms and
powers as factors.
[A] 4 4
log ( 8) logx x [B] 4 4
3log log ( 8)x x
[C] 4 4
log ( 8) 3logx x [D] 4 4 4
log log 8 3logx x
38. Solve the logarithmic equation: ln( ) ln 3 ln( 4)x x
[A] 4
3
[B] 6 [C] 6 [D] 4
3
7
39. Solve the rational inequality, express the solution in interval notation: 4
0 9
x
x
[A] ( 9, 4) [B] ( , 9) or 4,
[C] ( 9, ) [D] ( , 9)
40. If 6 6, and 5 4. Then ? f x x g x x g f x
[A] 30 34x [B] 30 26x [C] 30 34x [D] 30 30x
41. Find the amount that results from $1000 being invested at 5% compounded monthly after a period of
8 years. Use 1 . ntr
nA P
[A] $1702.09 [B] $1490.59 [C] $1400.00 [D] $400.00
42. How long will it take $2900 being invested at 7% compounded quarterly to double? Use
1 ntr
nA P and round to the nearest tenth of a year.
[A] 10.2 yr [B] 9.8 yr [C] 10.0 yr [D] 10.4 yr
43. Solve the system of equations: 3 5
. 2 3 8
x y
x y
If the system has no solution, choose inconsistent.
[A] (2, 1) [B] ( 1, 2) [C] (1, 2) [D] Inconsistent
44. List all potential rational zeros of the polynomial function 3 2
( ) 2 4 2 8f x x x x . (Do not find
the zeros.)
[A] 1
, , , 2
1 2 4 [B] 1 1
, , , , , 4 2
1 2 4 8
[C] 1 1 1
, , , , , , 8 4 2
1 2 4 8 [D] 1
, , , , 2
1 2 4 8
45. What rate of interest is required to triple an investment in 12 years if the interest is compounded
continuously? Use . r t
A Pe
[A] 3.976% [B] 8.006% [C] 9.155% [D] 12.983%
8
46. Given the piece-wise defined function
2
2
3 if 7 2
( ) 14 if 2
4 3 if 2
x x
f x x
x x
, determine the value (5).f
47. It is known that ( 4)x is a factor of the polynomial 3 2
( ) 4 4 16f x x x x . Find all the zeros
of ( )f x .
48. Identify the graph the system of inequalities: 3 1 3 1 3y x y x x
49. The reduced row echelon form of a system of linear equations is
1 2 0 6
0 1 3 5
0 0 1 3
. Write the
system of equations corresponding to the given matrix and then give the solution to the system.
50. Given the formula 2
2 2S r rh . Solve for h .
