The document is a college algebra final examination containing multiple-choice questions on various mathematical concepts such as loan interest, distance between points, equation of lines and circles, and graphical analysis. It also covers topics like function properties, transformations, rational inequalities, and investment calculations. The questions include practical applications and require knowledge of mathematical formulas and functions.

1. 1
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.
2

2. using interval notation.
interval notation.
64
5 5
64
5 5

3. 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,
[A] 14 [B] 26 [C] 169 [D] 13
9. List the intercepts for the graph of the equation
2
[A] ( 4, 0), (0,16)
2

4. 10. Find the slope-intercept form of the equation of the line that
is parallel with the given properties:
1
20
9
1
20
9
11. Write the standard from of the equation of the circle with
radius 5 and center (1, 4) .
2 2
2 2

5. 2 2
2 2
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
2
2
kc
I
d
2

6. kc
I
d
2
kd
I
c
, determine ( )( ).f g x
[A]
2
2
[C]
2
2

7. 14. The graph of a function f is given. For what values of x is
(
15. Determine whether the function
3 2
[A] Even [B] Odd [C] Neither [D] Both
16. Determine the average rate of change for the function
2
( ) ( )
.
f b f a
b a

8. [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

9. of x at which f has a local minimum.
18. Determine the function that is graphed after the following
transformations are applied to the graph of
of 3, and shifted vertically down 2
units.
19. Find and simplify the difference quotient,
( ) ( )
, 0
f x h f x
h
h

10. [A] 4 [B] 0 [C]
10
4
h
8( 5)
4
x
h
20. Suppose that
2
[A]
1
, 3
2

11. [B]
1
, 3
2
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 .
22. Determine the x-intervals where the function graphed at
the right is decreasing.
[A] decreasing on (5, 3.3)

12. 4
23. Identify the vertex of the graph of the function
2
24. Determine the quadratic function whose graph is given.
[A]
2

13. [B]
2
[C]
2
[D]
2
( ) ( 2) 1f x
25. The number of mosquitos ( )M x , in millions, in a certain
area depends on the June rainfall x , in
inches:
2
number of mosquitos?
[A] 0 inches [B] 5 inches [C] 100 inches [D] 10 inches

14. 26. Solve the inequality
2
27. Form a polynomial of degree 3 whose zeros are –5 with
multiplicity 2 and 4 with multiplicity 1.
[A] ( )
28. What are the x- and y-
2
[A]
-intercepts are ( 6, 0), (1, 0), (2, 0)
-intercept is (0,12)

15. 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)

16. -intercept is (0,12)
x
y
5
29. What is the domain of the rational function
2
2
( )
16
x
f x
x x
?

17. 30. Write the equation of all vertical asymptotes of the rational
function
2
2
( )
16
x
f x
x x
.
31. Write the equation of the horizontal asymptote of the
rational function
2

18. 2
( )
16
x
f x
x x
.
1
8
32. Which of the following displays a graph of a polynomial
multiplicity?
[A] [B]

19. [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

20. [B]
( ) as
( ) as
f x x
f x x
[C]
( ) as
( ) as
f x x
f x x

21. [D]
( ) as
( ) as
f x x
f x x
34. The function
2 1
( )
3
x
f x
-to-one. Find its inverse.
[A]
3 1
2
[B]

22. 3
[C]
3
2 1x
[D]
2 1
3
35. Solve the exponential equation
7 3 1
4
2
1
2

23. 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

24. 4 4
[C]
4 4
4 4 4
[A]
4
3
4
3

25. 7
39. Solve the rational inequality, express the solution in interval
notation:
4
0
9
x
x

26. 41. Find the amount that results from $1000 being invested at
5% compounded monthly after a period of
ntr
[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
ntr
[A] 10.2 yr [B] 9.8 yr [C] 10.0 yr [D] 10.4 yr
43. Solve the system of equations:

27. 3 5
.
2 3 8
x y
x y
If the system has no solution, choose inconsistent.
44. List all potential rational zeros of the polynomial function
3 2
d
the zeros.)
[A]
1
, , ,
2
1 1

28. , , , , ,
4 2
[C]
1 1 1
, , , , , ,
8 4 2
1
, , , ,
2
45. What rate of interest is required to triple an investment in
12 years if the interest is compounded
continuously? Use .
r t
[A] 3.976% [B] 8.006% [C] 9.155% [D] 12.983%

29. 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

30. 3 2
of ( )f x .
48. Identify the graph the system of inequalities: 3 1 3 1 3y x y
49. The reduced row echelon form of a system of linear

31. 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