MATH 101 FINAL EXAM PRINT ______________________ 12/17/08 NAME NO CALCULATOR ALLOWED. Part 1: In problems I - III, show work on this test paper. Put answers in the blanks provided. Work on scratch paper will NOT be graded. ___________________________________________________________________________________

I. Solve the equation 5x – 2(x + 3) = 4(5 – x) . Show how you got your answer.

Answer: _______________________________ II. Find all real solutions of x = 5x + 36 . Show how you got your answer.

Answer: _______________________________

III. Solve the system: 3x – 2y = –4x + 4y = 1

⎧⎨⎩

. Show how you got your answer.

Answer: _______________________________

2 Part 2: In the remaining problems, put the letter of the best answer on the answer sheet. ___________________________________________________________________________________

1. Simplify: (6ab–2 )

2ab–32

A. 9ba

B. – 9a3b7

C. 18b7

a3 D. 18a

b

2. Perform the indicated operation and simplify the result: (x + 2)(5x2 – x – 3) A. 5x3 + 9x2 – 5x – 6 B. 5x3 – 11x2 – x – 6 C. 5x3 + 9x2 + 5x – 6 D. 5x3 +11x2 + x – 6 3. Factor the expression 3x3 +14x2 – 5x completely. One of the factors is: A. (3x + 5) B. (x + 1) C. (x – 5) D. (3x – 1) 4. Find the quotient and remainder when x2 – 2x + 4 is divided by x – 5. A. x + 7, remainder 0 B. x + 7, remainder 4 C. x + 3, remainder 11 D. x + 3, remainder 19

5. Perform the indicated operations and simplify the result.

�

x – 2x

• x5

x2 + x – 6

A.

�

x4

x + 3 B.

�

x4

x – 3 C.

�

x6

x2 +1 D.

�

x6

x – 3

6. Perform the indicated operation and simplify. 3x –1

– 2x + 5

A. 1x –1

B. –2x + 5

C. x +17(x –1)(x + 5)

D. x +13(x –1)(x + 5)

7. Perform the indicated operation and simplify answer.

1x

1x+ 23

A. 31+ 2x

B. 33+ 2x

C. 23

D. 32

8. Rationalize the denominator and simplify answer. 26 + 3

A.

�

12 + 2 3–3

B.

�

12 – 2 333

C.

�

26– 2

3 D.

�

12 + 2 333

3 9. Simplify the expression: 7 5 + 2 20 A. –5 5 B. 9 5 C. 11 5 D. –11 5 10. Simplify the expression: (–27)2/3 A. 9 B. –9 C. –18 D. not a real number

11. Solve the equation: 3 – xx

+52=7x

A. – 38

⎧⎨⎩

⎫⎬⎭

B. {8} C. {–3} D. 83

⎧⎨⎩

⎫⎬⎭

12. Solve the equation: 2x3 – x2 + 6x – 3 = 0

A. – 12, ± 3⎧

⎨⎩

⎫⎬⎭

B. 12

⎧⎨⎩

⎫⎬⎭

C. – 12

⎧⎨⎩

⎫⎬⎭

D. 12, ± 3⎧

⎨⎩

⎫⎬⎭

13. Find all real solutions of the equation:

�

2x2 + x – 5 = 0

A.

�

–1– 412, –1+ 41

2

⎧ ⎨ ⎩

⎫ ⎬ ⎭

B.

�

–1– 414

, –1+ 414

⎧ ⎨ ⎩

⎫ ⎬ ⎭

C. 1– 394

, 1+ 394

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪ D. –1– 39

2, –1+ 39

2⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪ E. no real solution

14. Find all real solutions of the equation: 3x +13 = 2

A. 13

⎧⎨⎩

⎫⎬⎭

B. 73

⎧⎨⎩

⎫⎬⎭

C. 53

⎧⎨⎩

⎫⎬⎭

D.

�

272

⎧ ⎨ ⎩

⎫ ⎬ ⎭

E. no real solution

15. Solve the inequality: 5 – 3x ≤ x +17 A. [–3, ∞ ) B. ( –∞ , –3] C. (3, ∞ ) D. ( –∞ , 3] 16. Solve the inequality: 2x – 7 < 13

A. ( –∞ , –3) or (3, ∞ ) B. ( –∞ , –3) or (10, ∞ ) C. (–3, 10) D. (–3, 3) 17. Find the center (h, k) and the radius r of the circle with equation x2 + y2 + 4x + 6y = –9 . A. (h, k) = (–2, –3); r = 2 B. (h, k) = (2, 3); r = 4 C. (h, k) = (3, 2); r = 4 D. (h, k) = (–3, –2); r = 2

4 18. Find the slope-intercept equation of the line containing the points (1, 4) and (3, –2).

A. y = 13x +113

B. y = –3x +1 C. y = 13x + 5 D. y = –3x + 7

19. Find the slope-intercept equation of the line which is perpendicular to the line

�

y = 15x – 6 and

contains the point (4, –4).

A. y = –5x + 16 B. y = 5x –16 C.

�

y = – 15x – 16

5 D. y = –5x – 16

20. Find the domain of the function f (x) = 6 – x . A. {x: x > 6} B. {x: x ≠ 6} C. {x: x ≥ 6} D. {x: x ≤ 6} 21. Find the vertex of the quadratic function f (x) = 3x2 +12x –1 . A. (2, 37) B. (–2, 23) C. (2, 35) D. (–2, –13)

22. Find f(x + h) when

�

f (x) = 3x + 45x + 2

.

A.

�

3x + 7h5x + 7h

B.

�

3x + h + 45x + h + 2

C.

�

3x + 3h + 45x + 5h + 2

D.

�

3x + 3h + 25x + 5h

23. Find the inverse function of f (x) = 3x + 4 .

A. f −1 x( ) = 13x + 4

B. f −1 x( ) = x – 43

C. f −1 x( ) = x – 34

D. f −1 x( ) = –x + 25

E. f −1 x( ) = –x + 52

___________________________________________________________________________________ In problems #24 –25, match the equation with the graph which best represents it. Omit24. f (x) = x3 + 2 Omit25.

�

f (x) = x – 2 Omit26. f (x) = –x A. B. C.

D. E.

5 27. For the functions f (x) = 8x +13 and g(x) = 3x –1 , find the composite function ( f ! g)(x) . A. 24x + 5 B. 24x + 12 C. 24x + 21 D. 24x2 – 13 ___________________________________________________________________________________ In #28 - 30, use the graph shown below of a quadratic function y = f(x) with vertex at (–1, 4) and y-intercept at (0, 3). 28. Determine the equation of the graph.

A. y = x −1( )2 + 4 B. y = – x −1( )2 + 4 C. y = – x +1( )2 + 4 D. y = x +1( )2 + 4

E. y = – x +1( )2 – 4

Omit29. On what interval(s) is the function increasing? A. (–3, 1) B. (–∞, –3) C. (–1, ∞) D. (–∞, –1) E. (–∞, –3), (1, ∞) 30. What is the range of this function? A. [–3, 1] B. (–∞, –3), (1, ∞) C. (–4, ∞) D. [4, ∞) E. (–∞, 4] ___________________________________________________________________________________ 31. Solve the inequality (x + 2)(x – 5) > 0. A. (–2, –5) B. (–∞, –2) C. (–∞, –2), (5, ∞) D. (5, ∞) E. (–∞, 5), (–2, ∞) Omit32. The length of a rectangular picture frame is 5 centimeters longer than twice the width. If x represents the width of the frame, which of the following represents the area of the frame? A. A = 2x2 – 5x B. A = 6x +10 C. A = 4x2 +10x D. A = 2x2 + 5x 33. Which polynomial function defines the graph below?

A. f (x) = x +1( )2 (x – 2) B. f (x) = x +1( )(x – 2)2 C. f (x) = – x –1( )2 (x + 2) D. f (x) = – x +1( )(x – 2)2

E. f (x) = x –1( )2 (x + 2)2

6

34. Find any vertical asymptote(s) of f (x) = 2x – 7x2 – 4

.

A. x = 72

, x = 3 B. x = 2, x = –2 C. y = 2 D. y = 0

35. Find any horizontal asymptote of h(x) = 8x –162x + 5

.

A. y = 0 B. y = 4 C. x = – 52

D. y = –165

36. Find the exact value of log2 8 . A. 3 B. 256 C. 4 D. 8 E. 64

37. Solve for x: 35x = 19

A. 2 B. –2 C. – 25

D. 53

E. 27

_______5. Find the domain of the function f (x)= 12x−3 . Write answer in interval notation.

A. (0,4] B. −∞, 14

⎛⎝⎜

⎤⎦⎥

C. − 14,∞⎡

⎣⎢⎞⎠⎟ D. 1

4,∞⎡

⎣⎢⎞⎠⎟ E. (−∞, 4)∪ (4,∞)