Math Quiz 4 Review 1 Answer Key

4.1-4.3 Review Pre-Calculus Name:_______________________________________ Hour:_____ Graph the function (No graphing calculator! Use transformations on the parent function to graph!). State the domain, range, and asymptote. 1. 𝑓(𝑥) = 2𝑥+1 − 1 2. 𝑓(𝑥) = −2𝑥 + 3 3. 𝑓(𝑥) = 3 ∙ 2𝑥 Domain: Domain: Domain: Range: Range: Range: Asymptote: Asymptote: Asymptote: 4. 𝑓(𝑥) = 𝑒 𝑥−2 − 3 5. 𝑓(𝑥) = 𝑒 −𝑥 + 2 6. 𝑓(𝑥) = log 2 𝑥 + 1 Domain: Domain: Domain: Range: Range: Range: Asymptote: Asymptote: Asymptote: 7. 𝑓(𝑥) = log 2(𝑥 + 2) − 1 8. 𝑓(𝑥) = − log 2 (𝑥 − 1) 9. 𝑓(𝑥) = log 2(−𝑥) − 2 Domain: Domain: Domain: Range: Range: Range: Asymptote: Asymptote: Asymptote: 10. If $5000 is invested at an interest rate of 5% per year, find the value of the investment at the end of 5 years if it is compounded: a) annually b) quarterly c) continuously 11. If $2500 is invested at an interest rate of 2.5% per year, find the value of the investment at the end of 3 years if it is compounded: a) semi-annually b) monthly c) continuously 12. Find the exponential function y = 𝑎 𝑥 whose graph is given below. 13. Find the logarithmic function y = log 𝑎 𝑥 whose graph is given below. (9, 2) 1 (−1, ) 5 14. Find the logarithmic function y = log 𝑎 𝑥 whose graph is given below. 15. Find the exponential function y = 𝑎 𝑥 whose graph is given below. (5, 1) (−3, 27 ) 8 Find the domain of the function. 16. 𝑓(𝑥) = log(1 − 2𝑥) 17. 𝑓(𝑥) = log 5 (𝑥 + 4) 18. 𝑓(𝑥) = log 𝑥 + 1 19. 𝑓(𝑥) = log 2 (5 − 𝑥) 20. 𝑓(𝑥) = log 7 (𝑥 − 9) 21. 𝑓(𝑥) = log 𝑥 − 5 Write the equation in either exponential or logarithmic form. 22. 26 = 64 23. 𝑒 2𝑥 = 6 24. log 2 1024 = 10 25. ln 𝑥 = 17 26. log 2 128 27. log 8 1 28. 10log 45 29. ln 𝑒 6 30. log 9 27 31. log 3 32. log 5 √5 33. log 2 1623 34. 𝑒 2 ln 7 35. log(log 10100 ) Evaluate the expression. 1 81 1 36. ln 𝑒 37. log 8 0.25 Condense into a single logarithm and evaluate when possible. 38. log 25 + log 4 41. 3 log 2(𝑥 2 − 𝑦) − 2 log 2 (𝑥 + 𝑦) 39. log 8 3 − log 8 3 + log 8 2 1 2 42. 3 log 𝑥 + log 𝑥 − log 𝑥 40. log 6 + 4 log 2 43. 2(log 5 𝑥 + 2 log 5 𝑦 − 3 log 5 𝑧) Expand the expression. 44. log(9𝐶 5 ) 45. log 2 (2𝑥)2 𝑥2 46. ln √ 𝑎2 𝑥+1 𝑦 3 47. log 3 (𝑦𝑧2 ) 48. log 2 (𝑏4 𝑐) 49. log √3𝑟 2 𝑠 Answers: 1. 𝐷: (−∞, ∞); 𝑅: (−1, ∞); 𝑦 = −1 2. 𝐷: (−∞, ∞); 𝑅: (−∞, 3); 𝑦 = 3 3. 𝐷: (−∞, ∞); 𝑅: (0, ∞); 𝑦 = 0 4. 𝐷: (−∞, ∞); 𝑅: (−3, ∞); 𝑦 = −3 5. 𝐷: (−∞, ∞); 𝑅: (2, ∞); 𝑦 = 2 6. 𝐷: (0, ∞); 𝑅: (−∞, ∞); 𝑥 = 0 7. 𝐷: (−2, ∞); 𝑅: (−∞, ∞); 𝑥 = −2 8. 𝐷: (1, ∞); 𝑅: (−∞, ∞); 𝑥 = 1 9. 𝐷: (−∞, 0); 𝑅: (−∞, ∞); 𝑥 = 0 √ 10a. $6381.41; b. $6410.19; c. $6420.13 11a. $2693.46; b. $2694.50; c. $2694.71 12. y = 5x 13. 𝑦 = log 3 𝑥 15. 𝑦 = ( ) 18. (0, ∞) 19. (−∞, 5) 24. 210 = 1024 34. 49 43. log 5 ( 35. 2 𝑥𝑦 2 𝑧3 ) 2 20. (9, ∞) 25. e17 = x 36. -1 26. 7 37. − 44. log 9 + 5 log 𝐶 1 48. 2 log 2 𝑎 − 4 log 2 𝑏 − log 2 𝑐 2 2 𝑥 14. 𝑦 = log 5 𝑥 2 3 3 21. (0, ∞) 27. 0 38. 2 28. 45 39. 1 3 45. 2(log 2 2 + log 2 𝑥) 1 49. [log 3 + 2 log 𝑟 + log 𝑠] 3 1 16. (−∞, ) 2 22. log 2 64 = 6 29. 6 30. 17. (−4, ∞) 23. ln 6 = 2x 3 2 31. -4 3 40. 1.98 1 46. [ln(𝑥 + 1) − ln 𝑦] 2 (𝑥−𝑦)2 41. log 2 ((𝑥+𝑦)2) 32. 1 2 33. 92 𝑥4 42. log ( 1 ) 𝑥2 47. 2log 3 𝑥 − (log 3 𝑦 + 2log 3 𝑧)