In #1 and 2, use inverse operations to solve each equation. 1. 3x + 12 + 5x = 7 2. 1 (4x + 10) = x 5 2 3. Alex and Alyssa both have savings accounts. Alex has $515 and saves $23 per month. Alyssa has $725 and spends $20 per month. Which equation represents when Alex and Alyssa will have the same amount of money? F 515x + 23 = 725x 20 H 515 + 23x = 725 20x G 515x + 23 = 725x + 20 J 515 + 23x = 725 + 20x In #4 6, solve and graph each inequality. If you divide by a negative number, then the symbol will flip. 4. 4x + 6 2x < 1 5. 6 3 + x < 4 6. 2x + 10 10 or 3(x 4) 6 7. Use the graph at right to answer each question. a) Is the relation a function? b) Is the relation discrete or continuous? c) What is the domain? d) What is the range? 8. What is the range of the function f(x) = 1 x 1 when the domain is { 4, 2, 0, 2}? 2 9. For which value of x is the relation not a function {(0, 1), (x, 0), (3, 5), (2, 6)}? A 0 B 1 C 5 D 6
10. Which of the following does not represent y as a function of x? A B C D I only I and IV II and IV II and III 11. For g(x) = x 4, find g(x) when x = 3. 12. Evaluate f(x) = 3 5 x2 4 when x = 5. 13. The table shows the relationship between the number of lemons purchased and their cost. Lemons, x 1 2 3 4 Cost, y 0.1 0.2 0.3 0.4 Is the relationship a direct variation? F G H J Yes; it can be written as y = 0.1x. Yes; it can be written as y = 10x. No; it cannot be written as y = kx. No; the relationship is not a function. 14. The total amount of Wesley s paycheck varies directly with the number of hours he works. Wesley received a paycheck in the amount of $165 for working 20 hours. a) Write a direct variation equation for b) How much does Wesley earn if the amount of money y Wesley earns he works 83 hours this month at for working x hours. the bookstore? 15. Which of the following does not represent the equation of the graphed line? y A y 2x = 3 C y = 2x 3 B y + 2x = 3 D y 1 = 2(x 2) x
16. Which of the following is a correct statement about the relationship in the table? F The temperature is increasing 6 degrees each hour after 6 a.m. G The temperature is increasing 3 degrees each hour after 6 a.m. H The temperature is decreasing 6 degrees each hour after 6 a.m. J The temperature is decreasing 3 degrees each hour after 6 a.m. Hours after 6 A.M. Temperature in 2 30 4 36 6 42 8 48 17. Write an equation for the horizontal 18. Write an equation for the vertical line that passes through the point line that passes through the point (5, -2). (-6, -4). 19. Use the graph at right to answer each question. y a) Does the line have a positive or negative slope? b) What is the x-intercept? c) What is the y-intercept? x d) What is the equation of the line in slope-intercept form? 20. What is the x-intercept and y-intercept of 3x y = 15? A (-5, 0) and (0, -15) C (3, 0) and (0, -1) B (-5, 0) and (0, 15) D (0, -5) and (15, 0) 21. The graph shows the amount of water in a pool in relation to time. a) The pool is draining at a rate of gal each minute. This represents the of change or of the line. b) The pool will be empty in minutes. This represents the -intercept of the line. c) There were gallons in the pool before it was drained. This represents the -intercept of the line. 22. A line passes through (-8, 5) and is parallel to the graph of y = 1 x 2. 4 Write an equation to represent this line in slope-intercept form.
23. Which of the following is perpendicular to the graphed line? F y = 2x 3 G y = 2x + 4 H y = 1 x + 5 2 J y = 1 x 6 2 24. Which equation is equivalent to y + 3 = 6(x 5)? A 6x y = 27 C 6x + y = 27 B 6x y = 33 D 6x + y = 33 25. Sam is ordering pizza. Tony s Pizza charges $7 for a large cheese pizza plus $0.75 for each additional topping. Maria s Pizza charges $8 for a large cheese pizza plus $0.50 for each additional topping. a) Write a system of equations to b) For how many toppings will the cost be the represent this situation. same? { c) What will that cost be? 26. The perimeter of a rectangular wooden deck is 90 feet. The deck s length, l, is 5 feet less than 4 times its width, w. Which system of linear equations can be used to determine the dimensions, in feet, of the wooden deck? F l + w = 90 H 2l + 2w = 90 l = 5 4w l = 5 4w G 2l + 2w = 90 J l + w = 90 l = 4w 5 l = 4w 5 27. Which of the following graphs best represents a system of equations that has no solution?
28. Which inequality represents the graph? A y 3x 4 C y > 3x 4 B y 3x 4 D y < 3x 4 29. Which point is not in the solution set of the system of inequalities? { y < 4 x 2 Hint: Use the grid at right to graph the system before y choosing your answer. F (2, 0) H (-2, 0) x G (0, 0) J (-1, 4) 30. One model of a new car costs $18,000. Each year the car depreciates 10% in value. a) Write the exponential equation. b) Find the car s value in 5 years. 31. The number of student-athletes at a local high school is 1200 and is increasing at a rate of 2.6% per year. a) Write the exponential equation. b) How many student-athletes will there be in 4 years? In #32 34, simplify each expression. When multiplying like bases, keep the base and add the exponents. When dividing like bases, keep the base and subtract the exponents. You cannot leave your answer with a negative exponent move it! 32. ( 4x 5 ) 2 33. (4x 2 y) 2 ( 3xy 2 ) 0 34. 6x 8 y 3 z 2 3x 3 y 3 z 5 35. The length of a rectangle is (3x 2) and the width is (4x + 3). Find the area.
36. The length of a rectangle can be represented by (3x 2 1) and its width can be represented by (2x 2 5). What is the perimeter of the rectangle? 37. The area of a rectangular table is given by the trinomial 6x 2 + x 2. The table has a length of 2x 1. Find the width. Hint: You need to factor the trinomial. Multiply the first and last terms together, make a list of factors, etc. 38. Tiger Woods hits a golf ball into the air. The equation that describes the path of the ball in meters per second is h = 5t 2 + 55t, where h represents the height. Sketch a picture, and then use the axis of symmetry formula if needed. x = b You could also use your calculator. a) It takes the ball second(s) to reach its maximum height b) The ball s maximum height is meters. c) The ball is in the air a total of seconds. 2a 39. The height in feet of a rocket launched from the ground can be modeled by the function f(x) = 16x 2 + 96x, where x is the time in seconds after it is launched. Sketch a picture, and then use the axis of symmetry formula if needed. x = b You could also use your calculator. a) It takes the rocket seconds to reach its maximum height. b) The rocket s maximum height is feet. c) The rocket is in the air a total of seconds. 2a 40. Use the graph at right to answer the following questions. a) The axis of symmetry is x =. b) The vertex is (, ). c) The equation of the graph has zeros located at (, ) and (, ). d) The graph has a minimum/maximum value of. e) The domain is, and the range is.
41. Solve by using square roots. 42. Solve by using square roots. 0 = 180 2x 2 16x 2 5 = 44 43. Solve by factoring. 44. Solve by using the Quadratic Formula. 2x 2 15x + 7 = 0 2x 2 8x + 1 = 0 45. Compared to the graph of f(x) = 3x 4, the graph of g(x) = 1 x 1 is. 2 A B C D steeper and translated down 3 units steeper and translated up 3 units less steep and translated down 3 units less steep and translated up 3 units 46. If the graph of y = 2x 2 + 3 is shifted down 5 units, what will be the equation of the new graph? F y = 2x 2 2 H y = 2x 2 5 G y = 2x 2 + 8 J y = 3x 2 + 3
47. The solutions of a quadratic equation are -3 and 2. Write the standard form of a related quadratic function? In #48 and 49, use the descriptors to write the equation in vertex form. 48. Vertex is (-5, 3) 49. Vertex is (7, -1) Reflected across the x-axis Not reflected across the x-axis Vertically stretch by 2 Vertically compressed by 2 5 y = y = 50. The parabola is a translation of the quadratic parent function f(x) = x 2. Use the graph to write the equation in vertex form. y =