MATH 101 FINAL EXAM PRINT ______________________ 4/25/08 NAME NO CALCULATOR ALLOWED. Part 1: In problems 1 - 9, show work on this test paper. Put answers in the blanks provided. Work on scratch paper will NOT be graded. ___________________________________________________________________________________ 1. Factor the following expression completely: 2x 3 + 5x 2 + 2x . (5 pts.) Answer: ______________________________ 2. Find the quotient and remainder 2x 2 – 5x – 4 is divided by x – 2. Show how you got your answer. (5 pts.) Quotient: ___________________________ Remainder: ___________________________ 3. Add the following two rational expressions and simplify by combining like terms and factoring and 3 5x – 1 canceling terms if possible: . + x+2 x–3 (5 pts.) Answer: ______________________________ 4. Find the center (h, k) and the radius r of the circle with equation x 2 + y 2 + 2x – 6y – 6 = 0 . Show how you got your answer. (5 pts.) Center: __________________ A Radius: __________________ 2 5. Solve for x in the equation x + 3 = 4 x . What is/are the real solution(s)? Show how you got your answer. (5 pts.) Answer: ______________________________ 6. Solve for x in the following inequality and write your answer in interval notation: 3 – 5x < 13 . (5 pts.) Answer: ______________________________ 2x 7. Find the domain of the function f (x) = 2 . Show how you got your answer. x –1 (5 pts.) Answer: _____________________ 8. Find the domain of the function f (x) = x – 10 . Show how you got your answer. (5 pts.) Answer: _____________________ A 3 9. Use the graph of the function f shown below to answer parts (a) – (d). (a) Find f(–2). (3 pts.) Answer: __________ (b) What is the domain of f? (4 pts.) ____________________________ (c) For what numbers x is f(x) > 0? (4 pts.) ____________________________ (d) How often does the line y = 2 intersect the graph? (4 pts.) ____________________________ ___________________________________________________________________________________ Part 2: In the remaining problems, put the letter of the best answer on the answer sheet. (5 points each) 1. The diameter of a circle is 6 feet. Which of the following is the best estimate of the circle's area? A. 9 square feet B. 18 square feet D. 36 square feet C. 27 square feet E. 100 square feet 2. If a is –5 and b is –3, the value of 3a – 2b – 1 is which of the following? A. 5 B. 8 C. 10 1 5b10 5 b4 B. ( 4. Simplify the expression: 2x 3 y 2 A. 8x 9 y10 A E. 22 5b –8 b2 3. Simplify the expression: A. D. 12 B. C. ) 3 5 b10 D. 5b 6 E. 1 5b 6 y4 6x 6 y 20 C. 8x 6 y 24 D. 6x 9 y 20 ( 5. Simplify the expression: 16x A. 8x 7 ) 8x 28 B. 4 14 1/2 C. 4x12 D. 9x14 / 3 E. 4x 7 6. What are all the real solutions for x for the equation 2x 2 – 3x – 1 = 0 ? –3 + 5 –3 – 5 –2 + 17 –2 – 17 1 B. and C. and 4 4 6 6 2 3 + 17 3 – 17 D. and E. There are no real solutions 4 4 A. 1 and 7. The length of the hypotenuse of a right triangle is 10 cm and that the length of one of the other sides is 8 cm. What is the length of the third side? A. 5 cm B. 6 cm C. 8 cm D. 9 cm E. It cannot be determined from the information given 8. If 5 – 3(x – 1) = 6x + 1, then x equals: A. 7 9 B. 7 C. – 1 2 1 9 D. E. None of these 9. Perform the indicated operations and simplify the result. A. x4 x–3 B. x6 2 x +1 x6 x–3 C. D. 10. Rationalize the denominator and simplify your answer: A. 3+ 5 –2 B. 11. Simplify the expression: A. –9a 3 a 2 A 3– 5 –2 3 C. 5 –2 D. x–2 x5 • 2 x x + x–6 x4 x+3 5 x+3 E. 1 . 3– 5 3– 5 4 E. –27a 5 B. – 3a 3 a 2 C. –3a 2 3 a D. –9a 2 3 a 3+ 5 4 5 12. Determine whether the graph shown below is symmetric with respect to the x-axis, the y-axis, and/or the origin. A. origin only B. y-axis only C. x-axis only D. x-axis, y-axis, and origin E. None 13. Find the slope-intercept form of the equation of the line containing the points (–6, –7) and (4, –5). 29 1 1 29 1 29 A. y = 5x – B. y + 7 = (x + 6) C. y = – x – D. y = x – 5 5 5 5 5 5 ⎛ 7 ⎞ 14. Find an equation of the line with slope undefined and containing the point ⎜ – , 4 ⎟ . ⎝ 8 ⎠ 7 7 A. y = 4 B. y = – C. x = – D. x = 4 8 8 15. Find the slope-intercept form of the equation of the line parallel to the line y = –4x – 1 and containing the point (2, 6). A. y = 4x – 14 B. y = –4x + 14 C. y = –4x + 26 D. y = 4x – 26 16. Find f(x + h) when f (x) = –3x 2 – 4x + 5 . A. –3x 2 – 3xh – 3h 2 – 4x – 4h + 5 C. –3x 2 – 6xh – 3h 2 – 4x – 4h + 5 B. –3x 2 – 3h 2 – 4x – 4h + 5 D. –3x 2 – 3h 2 – 10x – 10h + 5 9x + 7 2x and g(x) = . Find (f + g)(x). 7x – 5 7x – 5 7x – 7 11x + 7 A. ( f + g)(x) = B. ( f + g)(x) = 7x – 5 7x – 5 11x – 7 –11x + 7 C. ( f + g)(x) = D. ( f + g)(x) = 7x – 5 7x – 5 17. Let f (x) = A 6 18. Find the midpoint of the line segment shown. A. (–1, 8) ⎛ 9 ⎞ B. ⎜ – , 2 ⎟ ⎝ 2 ⎠ 19. Find all intercepts of the graph with equation y = A. (–49, 0), (0, 0), (49, 0) C. (0, 0) C. (–9, 4) ⎛9 ⎞ D. ⎜ , 2 ⎟ ⎝2 ⎠ 7x . x + 49 2 B. (0, –7), (0, 0), (0, 7) D. (–7, 0), (0, 0), (7, 0) 20. Find the vertex of the quadratic function f (x) = x 2 + 6x – 1 . A. (3, –17) B. (–3, 17) C. (–3, –10) D. (3, 10) 21. Find the inverse function of f (x) = 5x + 3 . 1 x–3 x–5 A. f −1 ( x ) = B. f −1 ( x ) = C. f −1 ( x ) = 5x + 3 5 3 –x + 5 –x + 3 D. f −1 ( x ) = E. f −1 ( x ) = 3 5 22. For the functions f (x) = 8x + 13 and g(x) = 5x – 1 , find the composite function ( f ! g)(x) . A. 40x + 5 B. 40x + 12 C. 40x + 21 D. 40x 2 – 13 23. The graph of a quadratic function y = f(x) with vertex at (–1, 4) and y-intercept at (0, 3). Determine the equation of the graph. A. y = ( x − 1) + 4 2 B. y = – ( x − 1) + 4 2 C. y = – ( x + 1) + 4 2 D. y = ( x + 1) + 4 2 E. y = – ( x + 1) – 4 2 A 7 24. Solve the inequality (x + 5)(x + 2) > 0. A. (–5, –2) C. (2, ∞) B. (–∞, –5) D. (–∞, –2), (–5, ∞) E. (–∞, –5), (–2, ∞) 25. Which polynomial function defines the graph below? A. B. C. D. f (x) = ( x + 1) (x − 1)(x – 3) f (x) = – ( x + 1) (x − 1)(x – 3) f (x) = ( x + 1) (x − 1)(x + 3) f (x) = – ( x + 1) (x − 1)(x + 3) E. f (x) = ( x – 1) (x + 3) 2 26. Find any horizontal asymptote of f (x) = A. x = 7 2 B. x = 9 2x – 7 . x–9 C. y = 9 27. Find any vertical asymptotes of h(x) = D. y = 2 2x + 5 . 8x – 16 1 C. x = 2 4 28. Find the exact value of log 3 9 . A. y = 0 B. y = A. B. 2 3 C. 27 D. E. y = 0 D. x = – 18 5 2 E. 12 29. Solve for x: 2 x – 5 = 8 x A. A – 5 2 B. –4 C. 2 5 D. – 1 3 E. 8 E. x = 1 2