# Limit of a Function Essay

Pre-Calculus – Mid-Term Name_________________ 1. What is the solution region to the following function? f (x) > 2x + 4 + 3 A. Quadrant I only B. Quadrants I and III Quadrants II, III and IV C. Quadrants I and II 2. Determine which of the following relations is not a function. A. B. C. D. 3. Which defines the range of the following function: f (x) = x – 5 A. f (x) < 5 B. f (x) > –5 C. f (x) ? 5 D. f (x) ? –5 4. Write as one logarithm: 2log2x + 4log2y – 3log2z A. log2xyz B. log2x2 y4 z3 C. log2 z3 D. logxy 5. Which graph is a translation up and to the left of the parent function f (x) = – x

B. B. C. D. 6. The solutions to the following inequality are contained in which quadrants? 2(y + x) – 5 < 5(y + x) – 14 A. I, II and IIIB. I, III and IV C. I, II and IVD . II, III and IV 7. Which function models a translation 10 units down and 5 units right of the parent function f (x) = x A. f (x) = 5x – 10 B. f (x) = – 10x + 5 C. f (x) = x + 10 – 5 D. f (x) = x – 5 – 10 8. You have a final project for one of your courses. You have created a one-page title page, a one-page abstract, a one page table of contents, a 20 age body report, a one page summary, 7 pages of Appendices, and a one page bibliography. Your printer requires 2. 3 minutes to print 8 full pages of text at best quality mode. At this same rate, approximately how many minutes will the printer require to print your entire project at best quality mode? A. 17 B. 32 C. 9 D. 6 9. { f (x) = –[pic]x + 3 } is perpendicular and has the same y-intercept as: A. y + 20 = x + 26 B. 2y + 20 = 10x + 26 C. 2y = 10x D. y = 5x + 5 10. Describe the translation of the following graphs if f (x) is the original function. A. g(x) has been translated 3 units up and 4 units left to form f (x). B. (x) has been translated 4 units up and 3 units left to form g(x). C. g(x) has been translated 4 units down and 3 units right to form f (x). D. f (x) has been translated 3 units down and 4 units right to form g(x). 11. The solutions to the following system are contained in which quadrants? y > 2x + 5 y < –[pic]x – 3 A. II and IIIB. I, II, and III C. I, II and IVD . II, III and IV 12. If f (x) = x2 + x , and g(x) = x3 + 2x – 1 , find A. 35. 5 B. 69. 75 C. – 55 D. – 18. 25 13. Define the domain and range of the following piece-wise function: y A. Domain: (– 4 < x < 4 )B. Domain: (–3, –2, –1, 0 ) Range: (–3, –2, –1, 0 ) Range: (– 4 < y ? 4 ) C. Domain: (– 4 < x ? 4 )D. Domain: (–3, –2, –1, 0 ) Range: (–3, –2, –1, 0 ) Range: (– 4 < y < 4 ) 14. The expression x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y5 is the expansion of which of the following binomials? A. (x + y)6B. (x + y)5 (x – y)5D. (x – y)6 15. Determine the horizontal asymptote of the following function: f(x) = [pic] x = 5 y = 5 x = –7 y = –7 16.

Find the balance in an account at the end of 14 years if $5000 is invested at an interest rate of 9% that is compounded continuously. A. $16,998. 14 $17,234. 72 $17,627. 11 $17, 891. 23 17. Determine the number and type of solutions of the following polynomial function: f(x) = (x + 1)(x – 2)(x2 + 4) No real solutions B. 4 real C. 2 real and 2 imaginary D. 1 real and 2 imaginary 18. A rectangular container has a length of (x + 3) units. The volume of the container can be expressed by the following function: V(x) = x3 + 10×2 + 31x + 30. Which of the following could be an expression for the height of the container?

A. x + 1 B. x + 5C. x + 6 D. x + 10 19. Which binomial is not a factor of :x3 – x2 – 17x – 15 A. (x + 5) B. (x + 3) C. (x + 1) D. (x – 5) 20. What are the zeros of the polynomial function: y = (x – 3)(2x + 1)(x – 1)? A. {[pic], 1, 3}B. {–[pic], 1, 3} C. {–1, 1, 3}D. {–3, [pic], 1} 21. Which of the following is a root of: x4 – 2×2 – 12 A. i[pic] B. i[pic] C. 3 D. 1 22. Solve:x3 + 3×2 = x + 3 A. {–2, 1, 5}B. {1, 2, 3} C. {–5, 3, 7}D. {–3, –1, 1} 23. Determine the approximate solution(s) to the following system: y = x3 + x2 – 5x + 1 y = x A. (–3, –3)(0. 17, 0. 17)(2, 2) B. (–2, –2)( 0. 17, 0. 17)(3, 3) C. –1, –1)( 3, 3) D. (–3, –3)(2, 2) 24. Divide: x5 + 8×4 + 13×3 – 6×2 + 19x – 5 x + 5 A. x4 + 3×3 – 2×2 + 4x + 1 , R 2 B. x4 – 3×3 – 4×2 + 2x – 1 , R 2 C. x4 + 3×3 – 2×2 + 4x – 1 D. x4 – 3×3 – 4×2 + 2x + 1 25. Determine which equation best models the data in the table: x |-1 |0 |1 |2 |3. 5 |5. 5 |7. 5 |9 | |f (x) |2 |4 |5 |4 |2 |0. 5 |1 |3 | | A. f (x) = 0. 05×3 – 0. 575×2 + 1. 026x + 3. 9 B. f (x) = 0. 05×2 – 0. 575x + 1. 026x C. f (x) = 2×2 + 4x + 1 D. f (x) = 2x + 4 26. Determine the y-intercept for the following function: f (x) = x3 + 2×2 – x + 4 A. (0, – 4) B. (0, 4) C. (0, – 2)

D. (0, 2) 27. Determine how many real zeros the following function has: f (x) = x4 + 3×3 – 3x + 3 A. None B. Two C. Three D. One 28. Define the asymptote(s) for the following rational function: f(x) = [pic] A. vertical asymptote: (x = – 5 )C. vertical asymptote: (x = 2) horizontal asymptote: (y = 2)horizontal asymptote: (y = 5) vertical asymptote: (x = 5)D. vertical asymptote: (x = 2) horizontal asymptote: (y = 2)horizontal asymptote: (y = – 5) 29. Which defines the vertical asymptote(s) of the following function: f(x) = [pic] A. y = 5B. x = –5 C. y = 0 D. = ± 5 20. Describe the translation of the rational function if f(x) is the original function. A. f(x) has been translated 3 units up and 2 units left to form g(x). B. g(x) has been translated 2 units down and 3 left right to form f(x). C. f(x) has been translated 2 units up and 3 units right to form g(x). D. g(x) has been translated 3 units down and 2 units right to form f (x). 31. The branches of the rational function f(x) = [pic] are symmetric across which of the following lines: A. x – axisB. y – axis C. y = xD. y = –x 32. Determine the vertical asymptote(s) for the following rational function: pic] A. x = –2 , x = 3 B. x = –1 , x = –3 C. x = 1 , x = –3 D. x = 2 , x = 3 33. A relationship can be modeled by the following equation: y = [pic] Find x when y = 4. A. 6. 4 B. -11 C. 8. 1 D. 7 34. Write an equation for the graph of the rational function below: y x A. y = [pic]B. y = [pic] C. y = [pic]D. y = [pic] 35. State any points of discontinuity for the following rational function: [pic] A. [pic] B. [pic] C. [pic] D. The graph is continuous ———————– g(x) f (x) f (x) x y x y x y x y x x y y x x A. y y x2 y4 g(x) x x g(4) f (–2) 30. x x