What kind of number is? Write the number in scientific notation ,000
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1 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: What kind of number is? Write the number in scientific notation ,000 Write the number in standard form x Use a calculator to evaluate the expression. Round your answer to the nearest thousandth Find the midpoint of the line segment joining the two points. 6. (1,1) and (7,11)
2 Find the distance between the two points. 7. (1,1) and (4,5) If f(3) = -2 identify a point on the graph of f. Specify the domain of the function. 9. f(x) = 5x 2 + 4x f(x) = x 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 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?
3 2.1 Write a formula for this information slope = y-intercept = Use the table to find the regression line in the form y = ax + b X Y 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 x 8 = -7x + 18
4 19. x 5 3 2x Solve the inequalities symbolically x (4y 1) 20y 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 Use regression to find a quadratic function that best fits the data. Give results to the nearest hundredth. X F(x) F(x) =
5 3.2 Solve the quadratic equation. 25. x 2 + 9x x 2 + 8x + 1 = 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 x 2 4x 5 < 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 f(x) =
6 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 Predict the end behavior of the graph of f. 34. f(x) = x 2 2x 35. f(x) = 0.2x 5 7x Divide the first polynomial by the second and state the quotient and the remainder x 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 Find any vertical asymptotes. x f(x) = 5 2x
7 Find the horizontal asymptote of the given function. 4x f(x) = 2x Solve the equation x 3/2 + 5 = x 2/3 + 9x 1/ = Find the indicated composite for the pair of functions Given f(x) = and g(x) =, find (f g)(x) x 6 5x 43. Use the chart to answer the questions. x f(x) x g(x) 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
8 Determine whether or not the function is one-to-one. 45. f(x) = 8x 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) = ln x + ln x 2 = Solve for x. 50. e x+2 = 8 x 51. 3(2) x+2 = 99
9 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 ) Y(species) 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 x 5y = -38-4x + y = x y = 0 2xy = 4
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