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Algebra 2/Trig Name: ________________________________ CHAPTER 2 REVIEW Evaluate each expression by using the order of operations. 1. 5 + 2(7 – 4)2 6 3 4. ( ) 7 2. 36 x 52 – 3 x 42 3. 5 × 4 ÷ 2 + 3(4−1) 2 −2 3 5. 814 6. (− ) 5 State the property that is used in each statement. All variables represent real numbers. 7. 5n x 1 = 5n 8. 7d – 14 = 7(d – 2) 9. (a + b) + c = (b + a) + c 10. 4(yz) = (yz)4 Simplify each expression. No negative exponents in your final answer! (Assume no variable equals 0). 11. y3(x2y) 3𝑝4 𝑞−1 14. (8𝑝−2 𝑞3 )-2 12. (9rt)2 (3rst)-3 15. 13. 14𝑟 2 𝑠−3 𝑡 4 35𝑟 −2 𝑠5 𝑡 3 (𝑥 5 𝑦 7 )(𝑥 4 𝑦 −3 ) (𝑥 5 𝑦 3 )2 1 16. The cost of enrollment at a community college is $120 plus $75 per credit, c, taken. Express the college costs as a function of c and find the cost when 12 credits are taken. If Molly has a budget of $1300 per semester for tuition. How many credits can she take? State whether the following are functions, and if so give the domain and range. 17. {(5, 7), (7, 12), (9, 7), (11, 12), (13, 7)} 18. {(-2, 4), (0, 6), (-2, 8), (0, 10), (-2, 12)} Evaluate each function for x = -2, and x = 0 19. f(x) = 5x2 – 4x + 7 20. f(x) = 𝑥2 2 +𝑥−4 For questions 21 – 26, let f(x) = 2x + 7 and g(x) = x - 9. Find new functions and state any domain restrictions, if appropriate. 𝑔 21. f + g 22. 23. f ∙ g 24. g – f Evaluate each composite function. 25. (𝑔 𝑜 𝑓)(3) 26. (𝑓 𝑜 𝑔)(2) 𝑓 2 27. Find the inverse for the function. State whether the inverse is a function. {(1, 2), (5, 6), (2, 2), (6, 6), (3, 4)} Find an equation for the inverse and state whether the inverse is a function. 28. f(x) = 3𝑥−8 29. f(x) = x4 – 3 4 30. f(x) = x – ½ 31. Graph the function. f(x) = { 2𝑥 + 5 𝑖𝑓 𝑥 ≤ 0 1 − 3 𝑥 + 3 𝑖𝑓 𝑥 > 0 Evaluate: 32. [4.5] + 3.5 33. [−1.7] + [1.7] Identify each transformation from the parent function f to g. 34. f(x) = √𝑥, 𝑔(𝑥) = √𝑥 − 3 35. f(x) = x2, g(x) = (x + 3)2 – 4 3 Determine the equation of the transformed function. 36. The graph of f(x) = x2 is compressed horizontally by a factor of 1/2, reflected in the x-axis, and translated 4 units downward. 37. Write the equations for the function shown below. (Assume all tick marks represent 1 unit). a. b. c. d. 4