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Practice Exam 2 Name: Instructions: Give yourself 50 minutes to complete this practice exam. Justify each answer. 1. 12. 2. 13. 3. 14. 4. 15. 5. 16. 6. 17. 7. 18. 8. 19. 9. 20. 10. 21. 11. 22. 23. √ 24. 2 3 x + 1 -4 25. -3 26. 38 x + -2 4 4 3 3 2 2 1 1 -1 1 2 3 4 -3 -4 -3 -2 -1 -1 -1 -2 -2 -3 -3 -4 -4 √ 2 −x − 2 -4 1 2 1 2 3 4 1 2 3 4 27. −(x + 1)2 + 4 -2 4 4 3 3 2 2 1 1 -1 1 2 3 4 -4 -3 -2 -1 -1 -1 -2 -2 -3 -3 -4 -4 True or False For # 1-8, completely write either, ”True,” or, ”False.” 1. a(b + c) = ab + ac 2. (x + y)n = xn + y n 3. √ √ √ n x+y = nx+ ny 4. (xy)n = xn y n 5. 6. 7. √ √ √ n xy = n x n y n x y q n x y = = xn yn √ nx √ ny 8. −x5 + 2x2 − 7x + 12 has 6 roots. Algebra 9. Find x where (x − 5)3 − 5 = −10. 10. If g(x) is an invertible function, and g(4) = −2, what is the value of g −1 (−2)? 11. Find the inverse of f (x) = f (x) = x.) √ 3 7 − 3x. (You can check your answer by seeing if f −1 ◦ √ 12. What is the implied domain of g(x) = −3 2 6x − 8 − 18? (Your answer should be an interval.) 13. Suppose a 6= 0 and that b2 − 4ac ≥ 0. Write the following number as an integer in standard form: a −b − √ √ 2 b2 − 4ac −b − b2 − 4ac +b +c 2a 2a 14. Find 4x4 + x3 − x + 2 x2 + 1 15. Find 2x3 − 15x − 6 x−3 16. What is the slope of the straight line in R2 that passes through the points (1, −4) and (−2, −5). 17. Complete the square: Write −2x2 −4x+7 in the form α(x+β)2 +δ where α, β, δ ∈ R. 18. How many roots does 7x2 − 12x + 5 have? 19. Find the roots of −3x2 − 3x + 15. 20. Find a root of x3 + 3x2 − 6x + 8. 21. Completely factor 3x3 + 15x2 + 23x + 15. (Hint: -3 is a root.) Your answer should be a product of a constant polynomial and some number of linear and quadratic polynomials that are monic, and any of the quadratic polynomials should have no roots. 22. Completely factor −2x3 + 4x2 + 24x + 30 (Hint: 5 is a root.) Your answer should have the same form as described in the previous problem. Graphs 23. List all of the monic linear factors of p(x) that you know of from the graph below. -6 -5 -4 -3 -2 -1 1 √ 24. Graph 2 3 x + 1 and label its x− and y−intercepts. 25. Graph √ 2 −x − 2 and label its x− and y−intercepts. 26. Graph 83 x + 1 2 and label its x− and y−intercepts. 27. Graph −(x + 1)2 + 4 and label its vertex. 2 3 4 5 6