Chapter 1: 1.1, 1.2, 1.3, 1.4 Chapter 2: 2.1, 2.2, 2.3, 2.4 Chapter 3: 3.1, 3.2, 3.3, 3.4 Chapter 4: 4.1, 4.2, 4.3, 4.5, 4.7 Chapter 5: 5.1, 5.2, 5.3, 5.4, 5.6, 5.7 Chapter 6: 6.1 1.1 What kind of number is? 1. -563 2. 64.9 Write the number in scientific notation. 3. 850,000 Write the number in standard form. 4. 9.11 x 10 8 1.2 Use a calculator to evaluate the expression. Round your answer to the nearest thousandth. 4 5. 368 Find the midpoint of the line segment joining the two points. 6. (1,1) and (7,11)
Find the distance between the two points. 7. (1,1) and (4,5) 1.3 8. If f(3) = -2 identify a point on the graph of f. Specify the domain of the function. 9. f(x) = 5x 2 + 4x + 8 1 10. f(x) = x 7 1.4 Find the slope of the line between the two points. 11. (4,6) and (2,5) What is the slope of the graph of f? 12. f(x) = 4x + 7 13. A train is initially 130 miles from a station and moved toward the station at 34 mph. Write a function f that calculates the distance that the train is from the station after x hours. f(x) = How far is the train from the station after 3 hours?
2.1 Write a formula for this information. 2 7 14. slope = y-intercept = 5 3 15. Use the table to find the regression line in the form y = ax + b X 50 60 70 80 90 Y 160 163 163 166 167 Window [45, 100, 10] by [155,170,10] y = Estimated value for y when x=56? 2.2 What are the x and y intercepts of the equation? 16. 2x 5y = 10 Find an equation for a line parallel to y = 5x -2 through the point (3,4). 17. y = 2.3 Solve the equations. 18. 6x 8 = -7x + 18
19. x 5 3 2x 3 2 5 4 2.4 Solve the inequalities symbolically. 20. 1 3x 6 8 21. 4(4y 1) 20y 16 3.1 Determine the vertex of the graph of f. 22. f(x) = 4x 2 16x + 21 Write the equation as f(x) = a(x-h) 2 + k. 23. f(x) = x 2 + 6x 4 24. Use regression to find a quadratic function that best fits the data. Give results to the nearest hundredth. X -2.4 34.8 65.6 102.3 253.6 F(x) 999.9 123.4 45.6 230.5 899.5 F(x) =
3.2 Solve the quadratic equation. 25. x 2 + 9x + 20 26. 3x 2 + 8x + 1 = 0 27. A piece of cardboard is 6 inches longer than it is wide. Cutting out 2-inch squares from the corners makes a box with a volume of 224in 3. What are the dimensions of the cardboard? 3.3 Solve the inequality. 28. x 2 + x -9 0 29. x 2 4x 5 < 0 3.4 Answer the question. 30. How can the graph of f(x) = (x 2) 2 5 be obtained from the graph of y = x 2? Write an equation for a graph with the slope of y = x 3, but is shifted left 7 units and shrunk vertically by a factor of 0.68. 31. f(x) =
4.1 Determine where the function f(x) is increasing and decreasing 32. f(x) = x 3 4x 2 + x + 5 Determine any local extrema and absolute extrema. 33. g(x) = -4x 2 24x 39 4.2 Predict the end behavior of the graph of f. 34. f(x) = x 2 2x 35. f(x) = 0.2x 5 7x 2 + 1 4.3 Divide the first polynomial by the second and state the quotient and the remainder. 36. 2x 3 + 3x 2 + 4x -10, x + 1 Use the remainder theorem to find the remainder when f(x) is divided by the given x k. 37. f(x) = 4x 3 2x 2 + 8x + 24; x -2 4.5 Find any vertical asymptotes. x 6 38. f(x) = 5 2x
Find the horizontal asymptote of the given function. 4x 1 39. f(x) = 2x 6 4.7 Solve the equation. 40. 4x 3/2 + 5 = 21 41. x 2/3 + 9x 1/3 + 14 = 0 5.1 Find the indicated composite for the pair of functions. 4 3 42. Given f(x) = and g(x) =, find (f g)(x) x 6 5x 43. Use the chart to answer the questions. x 1 2 3 4 f(x) 4 3 1 2 x 1 2 3 4 g(x) 2 3 4 5 a) (g f)(1) b) (f g)(4) c) (f f)(3) 5.2 Find a symbolic representation for f -1 (x). x 44. f(x) = x 2
Determine whether or not the function is one-to-one. 45. f(x) = 8x 2 + 5 5.3 Find C and a so that f(x) = Ca x satisfies the given conditions. 46. f(1) = 6 and for each unit increase in x, the output is multiplied by 5 4 Use the compound interest formula to determine the final value of the given amount. 47. $14,000 at 11% compounded semiannually for 13 years 5.4 Solve for x. 48. log 3 (1 x) = 1 49. ln x + ln x 2 = 3 5.6 Solve for x. 50. e x+2 = 8 x 51. 3(2) x+2 = 99
5.7 52. Near New Guinea there is a relationship between the number of bird species found on an island and the size of the island. The accompanying table lists numbers of species of birds y found on an island with an area of x square kilometers. X(km 2 ) 0.1 1 10 100 1000 Y(species) 10 15 20 25 30 a) Find a function f that models the data. b) Predict the number of bird species on an island of 5000 square kilometers. 6.1 Solve the equation for x and then solve it for y. 2x y 53. = 1 3y Solve the system of linear equations. 54. 3x 5y = -38-4x + y = 28 55. 2x y = 0 2xy = 4