Section 7.1 (Page 424, Textbook):

5,11,15,21,23,25,27,29,31,33,35,37,39,41,43

CHAPTER 7: Algebra: Graphs, Functions, and Linear Systems 424 Chapter 7 Algebra: Graphs, Functions, and Linear Systems Exercise Set 7.1 Practice Exercises In Exercises 1-20, plot the given point in a rectangular coordinate system. 1. (1, 4) 2. (2, 5) 49. f(x) = x - 1 50. f(x) = x+1 3. (-2, 3) 4. (-1, 4) * f ( x) = x-1 f ( x) = x+1 5. (-3, -5) 6. (-4, -2) -2 -2 7. (4, -1) 8. (3, -2) -1 -1 9. (-4, 0) 10. (-5, 0) 0 11. (0, -3) 12. (0, -4) 1 1 13. (0, 0) 14. (-3, -14) 2 2 15. (-2, -34) 16. (-5, -2.5) 17. (3.5, 4.5) 18. (2.5, 3.5) 51. f(x) = (x - 2)2 52. f(x) = (x + 1)2 19. (1.25, -3.25) 20. (2.25, -4.25) * f ( x) = (x - 2)2 f ( x ) = ( x+1)2 Graph each equation in Exercises 21-32. Select integers for x from 0 -3 -3 to 3, inclusive. -2 21. y = x2 - 2 22. y = x2 + 2 2 -1 23. y = x - 2 24. y = x + 2 0 25. y = 2x + 1 26. y = 2x - 4 1 27. y = -x 28. y = -fx + 2 53. f(x) = x3 + 1 54. f(x) = (x+ 1)3 29. y = x3 30. y = x3 - 1 f( x) = x3+1 * f ( x ) = (x+ 1)3 31. y = [x| + 1 32. y = [x| - 1 x -3 In Exercises 33-46, evaluate each function at the given value of the variable. -2 33. f(x) = x - 4 a. f(8) b. f(1) 34. f(x) = x - 6 a. f(9) b. f(2) - 35. f(x) = 3x - 2 a. f(7) b. f(0) 36. f(x) = 4x - 3 a. f(7) b. f(0) For Exercises 55-62, use the vertical line test to identify graphs in 37. g(x) = x2 + 1 a. g(2) b. 8(-2) which y is a function of x. 38. g(x) = x2 + 4 a. g(3) b. g(-3) 55. 56. 39. g(x) = -x2 + 2 a. g(4) b. g(-3) 40. 8(x) = -x2 + 1 a. g(5) b. 8(-4) 41. h(r) = 3r2 + 5 a. h(4) b. h(-1) 42. h(r) = 2r2 - 4 a. h(5) b. h(-1) * 43. f(x) = 2x2 + 3x - 1 a. f(3) b. f(-4) 44. f(x) = 3x2 + 4x - 2 a. f(2) b. f(-1) 57. 58. 45. f (x) = a. f(6) b. f(-6) 46. f(x) = x x a. f(5) b. f(-5) In Exercises 47-54, evaluate f (x) for the given values of x. Then use the ordered pairs (x, f(x)) from your table to graph the function. 47. f(x) = x2 - 1 48. f (x) = x2 + 1 * f ( x ) = x - 1 * f ( x) = x +1 59 60. -2 - 2 1-1 0 0 1 1 2 2CHAPTER 7: Algebra: Graphs, Functions, and Linear Systems Section 7.2 Linear Functions and Their Graphs 437 Concept and Vocabulary Check Fill in each blank so that the resulting statement is true. Cl. The x-coordinate of a point where a graph crosses the C5. The slope of the linear function whose equation is x-axis is called a/an _ f(x) = -4x + 3 is and the y-intercept of its graph C2. The point (0, 3) lies along a line, so 3 is a/an of is _ that line. C6. In order to graph the line whose equation is y = =x + 3, C3. The slope of the line through the distinct points (x], y, ) begin by plotting the point From this point, and (X2, )2 ) is we move _ units up (the rise) and units to the C4. The slope-intercept form of the equation of a line is right (the run). where m represents the and C7. The graph of the equation y = 3 is alan_ line. b represents the C8. The graph of the equation x = -2 is alan line. Exercise Set 7.2 Practice Exercises In Exercises 33-40, In Exercises 1-8, use the x- and y-intercepts to graph each linear a. Put the equation in slope-intercept form by solving for y. equation. b. Identify the slope and the y-intercept. c. Use the slope and y-intercept to graph the line. 1. x- y = 3 2. xty =4 33. 3x + y = 0 34. 2x + y = 0 3. 3x - 4y = 12 4. 2x - 5y = 10 35. 3y = 4x 36. 4y = 5.x 5. 2x + y = 6 6. x + 3y = 6 37. 2x + y = 3 38. 3x + y = 4 7. 5x = 3y - 15 8. 3x - 2y + 6 39. 7x + 2y = 14 40. 5x + 3y = 15 In Exercises 9-20, calculate the slope of the line passing through the given points. If the slope is undefined, so state. Then indicate In Exercises 41-48, graph each horizontal or vertical line. whether the line rises, falls, is horizontal, or is vertical. 41. y = 4 42. y = 2 9. (2, 6) and (3, 5) 13. y = -2 44. y = -3 10. (4, 2) and (3, 4) 45. x = 2 46. x = 4 11. (-2, 1) and (2, 2) 47. x + 1 = 0 48. x + 5 = 0 12. (-1, 3) and (2, 4) 13. (-2, 4) and (-1, -1) Practice PLUS 14. (6, -4) and (4, -2) In Exercises 49-52, find the slope of the line passing through each 15. (5, 3) and (5, -2) pair of points or state that the slope is undefined. Assume that all variables represent positive real numbers. Then indicate whether 16. (3, -4) and (3, 5) the line through the points rises, falls, is horizontal, or is vertical. 17. (2, 0) and (0, 8) 49. (0, a) and (b, 0) 18. (3, 0) and (0, -9) 50. (-a, 0) and (0, -b) 19. (5, 1 ) and (-2, 1) 51. (a, b) and (a, b + c) 20. (-2, 3) and (1, 3) 52. (a - b, c) and (a, a + c) In Exercises 21-32, graph each linear function using the slope and In Exercises 53-54, find the slope and y-intercept of each line y-intercept. whose equation is given. Assume that B = 0. 21. y = 2x + 3 22. y = 2x + 1 53. Ax + By = C 23. y = -2x + 4 24. y = -2x + 3 54. Ax = By - C 25. y = fx + 3 26. y = fx + 2 In Exercises 55-56, find the value of y if the line through the two 27. f(x) = 3x - 4 28. f(x) = 4x - 5 given points is to have the indicated slope. 29. y = -1x + 4 30. y = -fx + 5 55. (3, y) and (1, 4), m = -3 31. f (x) = -3x 32. f (x ) = -fx 56. (-2, y) and (4, -4), m = }