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 .

Basic features

- Free title page and bibliography
- Unlimited revisions
- Plagiarism-free guarantee
- Money-back guarantee
- 24/7 support

On-demand options

- Writer’s samples
- Part-by-part delivery
- Overnight delivery
- Copies of used sources
- Expert Proofreading

Paper format

- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)