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Math 1050 Practice Exam 3 a April 6, 2012 Answer all questions below. Every question is worth the same number of points. You may use the available space for work, but must write ALL answers on the answer sheet. No cell phones, calculators, or notes are allowed during the exam. These rules will be strictly enforced. Name: ___________________________________________________________ Number: Rational Functions: 1. Completely factor the numerator of the rational function 3x2 + 2x x—3 — 2. Find the zeros for the rational function [email protected] 3)(x + 4) z—4 3. Find the vertical asymptotes of the rational function 3~ + 1)(z 5) (x-7)(z-6) — 4. Calculate the end behavior of ((x-7)(z-2) 2(x + 4) — Implied Domain: 5. What is tile implied domain of f(x) = iog9(x + 4)? 6. What is the implied domain of g(x) = ~ + 5)~ x(x—5) 7. What is the implied domain of li(x) = ~ flanslating: Logarithms ~ Exponentials 8. Write iog4(x + 1) 9. Write 24x2 = = as an exponential equation. 22 as a logarithmic equation. Page 2 Rewriting Logarithms: 10. Rewrite log7(z) — log7(yx) + log7(xz) as a single logarithm. 11. Rewrite log12(~’) as the sum and difference of several more basic logarithms. 12. Rewrite log4(44) using logarithms with base 10. 13. What is the integer part of log4(74)? Solving Equations: 14. Solve for x: log4(4x) 15. Solveforx: — log4fr — 2) = 2 4X+19....7+3x4Z Page3 Application 16. Suppose you buy a Hybrid. It costs 18, 000 dollars. If it depreciates at 3 percent per year. What is its value after t years? Algebra 17. Write @2 as a single power of a. 18. Evaluate f(4) given that f(x) = { ~ Page 4 x e[4,~) Graphs f C) = 20. (2 points) Graph li(x) = 4x• 21. (2 points) Graph g(~) = log3(x). Label any x-intercepts. Label any y-intercepts. 22. (2 points) Graph k(x) = 19. (4 points) Graph 23. (2 pomts) Graph 1(x) = 3(a ±2)(z 2)x Label Ml important information. Label any x-intereepts. Label any y-intercepts. + 4. Label any x-intercepts. Label any y-intercepts. log7(x — 3). Label any x-intercepts. Label any y-intercepts. 24. Suggest a restaurant. Page 5 N u ii I (3 ‘~ ~. 11. to t~(~~) i~) ~. ./ 3. 12. ~ —1. c3 13. ~j (~ 5. 6. 11. ~c/o 15. 1R 16. 3_~ ~Z (o~ 8. 9. 17. ~ k~j~ 18. Page 6 (~D ie,~( HO3)~ ~ ~1b 3 ~ 17 a I Cf ( x=S