1. How do you solve an absolute value equation?\r\n\r\n2.\u00a0How can you tell whether an absolute value function has two x-intercepts without graphing the function?\r\n\r\n3. When solving an absolute value function, the isolated absolute value term is equal to a negative number. What does that tell you about the graph of the absolute value function?\r\n\r\n4.\u00a0How can you use the graph of an absolute value function to determine the x-values for which the function values are negative?\r\n\r\n5. How do you solve an absolute value inequality algebraically?\r\n\r\n6.\u00a0Describe all numbers [latex]x[\/latex] that are at a distance of 4 from the number 8. Express this using absolute value notation.\r\n\r\n7. Describe all numbers [latex]x[\/latex] that are at a distance of [latex]\\frac{1}{2}[\/latex] from the number \u22124. Express this using absolute value notation.\r\n\r\n8.\u00a0Describe the situation in which the distance that point [latex]x[\/latex] is from 10 is at least 15 units. Express this using absolute value notation.\r\n\r\n9. Find all function values [latex]f\\left(x\\right)[\/latex] such that the distance from [latex]f\\left(x\\right)[\/latex] to the value 8 is less than 0.03 units. Express this using absolute value notation.\r\n\r\nFor the following exercises, solve the equations below and express the answer using set notation.\r\n<\/p>
10. [latex]|x+3|=9[\/latex]<\/span><\/p>\r\n 11. [latex]|6-x|=5[\/latex]<\/span><\/p>\r\n 12.\u00a0[latex]|5x - 2|=11[\/latex]<\/span><\/p>\r\n 13. [latex]|4x - 2|=11[\/latex]<\/span><\/p>\r\n 14.\u00a0[latex]2|4-x|=7[\/latex]<\/span><\/p>\r\n 15. [latex]3|5-x|=5[\/latex]<\/span><\/p>\r\n 16.\u00a0[latex]3|x+1|-4=5[\/latex]<\/span><\/p>\r\n 17. [latex]5|x - 4|-7=2[\/latex]<\/span><\/p>\r\n 18.\u00a0[latex]0=-|x - 3|+2[\/latex]<\/span><\/p>\r\n 19. [latex]2|x - 3|+1=2[\/latex]<\/span><\/p>\r\n 20.\u00a0[latex]|3x - 2|=7[\/latex]<\/span><\/p>\r\n 21. [latex]|3x - 2|=-7[\/latex]<\/span><\/p>\r\n 22.\u00a0[latex]\\left|\\frac{1}{2}x - 5\\right|=11[\/latex]<\/span><\/p>\r\n 23. [latex]\\left|\\frac{1}{3}x+5\\right|=14[\/latex]<\/span><\/p>\r\n 24.\u00a0[latex]-\\left|\\frac{1}{3}x+5\\right|+14=0[\/latex]<\/span><\/p>\r\n For the following exercises, find the x- and y-intercepts of the graphs of each function.<\/span><\/p>\r\n 25. [latex]f\\left(x\\right)=2|x+1|-10[\/latex]<\/span><\/p>\r\n 26.\u00a0[latex]f\\left(x\\right)=4|x - 3|+4[\/latex]<\/span><\/p>\r\n 27. [latex]f\\left(x\\right)=-3|x - 2|-1[\/latex]<\/span><\/p>\r\n 28.\u00a0[latex]f\\left(x\\right)=-2|x+1|+6[\/latex]<\/span><\/p>\r\n For the following exercises, solve each inequality and write the solution in interval notation.<\/span><\/p>\r\n 29. [latex]\\left|x - 2\\right|>10[\/latex]<\/span><\/p>\r\n 30.\u00a0[latex]2|v - 7|-4\\ge 42[\/latex]<\/span><\/p>\r\n 31. [latex]|3x - 4|\\le 8[\/latex]<\/span><\/p>\r\n 32.\u00a0[latex]|x - 4|\\ge 8[\/latex]<\/span><\/p>\r\n 33. [latex]|3x - 5|\\ge 13[\/latex]<\/span><\/p>\r\n 34.\u00a0[latex]|3x - 5|\\ge -13[\/latex]<\/span><\/p>\r\n 35. [latex]\\left|\\frac{3}{4}x - 5\\right|\\ge 7[\/latex]<\/span><\/p>\r\n 36.\u00a0[latex]\\left|\\frac{3}{4}x - 5\\right|+1\\le 16[\/latex]<\/span><\/p>\r\n For the following exercises, graph the absolute value function. Plot at least five points by hand for each graph.<\/span><\/p>\r\n 37. [latex]y=|x - 1|[\/latex]<\/span><\/p>\r\n 38.\u00a0[latex]y=|x+1|[\/latex]<\/span><\/p>\r\n 39. [latex]y=|x|+1[\/latex]<\/span><\/p>\r\n For the following exercises, graph the given functions by hand.<\/span><\/p>\r\n 40. [latex]y=|x|-2[\/latex]<\/span><\/p>\r\n 41. [latex]y=-|x|[\/latex]<\/span><\/p>\r\n 42. [latex]y=-|x|-2[\/latex]<\/span><\/p>\r\n 43. [latex]y=-|x - 3|-2[\/latex]<\/span><\/p>\r\n 44.\u00a0[latex]f\\left(x\\right)=-|x - 1|-2[\/latex]<\/span><\/p>\r\n 45. [latex]f\\left(x\\right)=-|x+3|+4[\/latex]<\/span><\/p>\r\n 46. [latex]f\\left(x\\right)=2|x+3|+1[\/latex]<\/span><\/p>\r\n 47. [latex]f\\left(x\\right)=3|x - 2|+3[\/latex]<\/span><\/p>\r\n 48.\u00a0[latex]f\\left(x\\right)=|2x - 4|-3[\/latex]<\/span><\/p>\r\n 49. [latex]f\\left(x\\right)=|3x+9|+2[\/latex]<\/span><\/p>\r\n 50.\u00a0[latex]f\\left(x\\right)=-|x - 1|-3[\/latex]<\/span><\/p>\r\n 51. [latex]f\\left(x\\right)=-|x+4|-3[\/latex]<\/span><\/p>\r\n 52.\u00a0[latex]f\\left(x\\right)=\\frac{1}{2}\\left|x+4\\right|-3[\/latex]<\/span><\/p>\r\n 53.\u00a0Use a graphing utility to graph [latex]f\\left(x\\right)=10|x - 2|[\/latex] on the viewing window [latex]\\left[0,4\\right][\/latex]. Identify the corresponding range. Show the graph.<\/span><\/p>\r\n 54.\u00a0Use a graphing utility to graph [latex]f\\left(x\\right)=-100|x|+100[\/latex] on the viewing window [latex]\\left[-5,5\\right][\/latex]. Identify the corresponding range. Show the graph.<\/span><\/p>\r\n For the following exercises, graph each function using a graphing utility. Specify the viewing window.<\/span><\/p>\r\n 55. [latex]f\\left(x\\right)=\\left(-0.1\\right)\\left|0.1\\left(0.2-x\\right)\\right|+0.3[\/latex]<\/span><\/p>\r\n 56.\u00a0[latex]f\\left(x\\right)=4\\times {10}^{9}\\left|x-\\left(5\\times {10}^{9}\\right)\\right|+2\\times {10}^{9}[\/latex]<\/span><\/p>\r\n For the following exercises, solve the inequality.<\/span><\/p>\r\n 57. [latex]\\left|-2x-\\frac{2}{3}\\left(x+1\\right)\\right|+3>-1[\/latex]<\/span><\/p>\r\n 58.\u00a0If possible, find all values of [latex]a[\/latex] such that there are no [latex]x\\text{-}[\/latex] intercepts for [latex]f\\left(x\\right)=2|x+1|+a[\/latex].<\/span><\/p>\r\n 59. If possible, find all values of [latex]a[\/latex] such that there are no [latex]y[\/latex] -intercepts for [latex]f\\left(x\\right)=2|x+1|+a[\/latex].<\/span><\/p>\r\n 60.\u00a0Cities A and B are on the same east-west line. Assume that city A is located at the origin. If the distance from city A to city B is at least 100 miles and [latex]x[\/latex] represents the distance from city B to city A, express this using absolute value notation.<\/span><\/p>\r\n 61. The true proportion [latex]p[\/latex] of people who give a favorable rating to Congress is 8% with a margin of error of 1.5%. Describe this statement using an absolute value equation.<\/span><\/p>\r\n 62.\u00a0Students who score within 18 points of the number 82 will pass a particular test. Write this statement using absolute value notation and use the variable [latex]x[\/latex] for the score.<\/span><\/p>\r\n 63. A machinist must produce a bearing that is within 0.01 inches of the correct diameter of 5.0 inches. Using [latex]x[\/latex] as the diameter of the bearing, write this statement using absolute value notation.<\/span><\/p>\r\n 64.\u00a0The tolerance for a ball bearing is 0.01. If the true diameter of the bearing is to be 2.0 inches and the measured value of the diameter is [latex]x[\/latex] inches, express the tolerance using absolute value notation.<\/span><\/p>","rendered":" 1. How do you solve an absolute value equation?<\/p>\n 2.\u00a0How can you tell whether an absolute value function has two x-intercepts without graphing the function?<\/p>\n 3. When solving an absolute value function, the isolated absolute value term is equal to a negative number. What does that tell you about the graph of the absolute value function?<\/p>\n 4.\u00a0How can you use the graph of an absolute value function to determine the x-values for which the function values are negative?<\/p>\n 5. How do you solve an absolute value inequality algebraically?<\/p>\n 6.\u00a0Describe all numbers [latex]x[\/latex] that are at a distance of 4 from the number 8. Express this using absolute value notation.<\/p>\n 7. Describe all numbers [latex]x[\/latex] that are at a distance of [latex]\\frac{1}{2}[\/latex] from the number \u22124. Express this using absolute value notation.<\/p>\n 8.\u00a0Describe the situation in which the distance that point [latex]x[\/latex] is from 10 is at least 15 units. Express this using absolute value notation.<\/p>\n 9. Find all function values [latex]f\\left(x\\right)[\/latex] such that the distance from [latex]f\\left(x\\right)[\/latex] to the value 8 is less than 0.03 units. Express this using absolute value notation.<\/p>\n For the following exercises, solve the equations below and express the answer using set notation.\n<\/p>\n 10. [latex]|x+3|=9[\/latex]<\/span><\/p>\n 11. [latex]|6-x|=5[\/latex]<\/span><\/p>\n 12.\u00a0[latex]|5x - 2|=11[\/latex]<\/span><\/p>\n 13. [latex]|4x - 2|=11[\/latex]<\/span><\/p>\n 14.\u00a0[latex]2|4-x|=7[\/latex]<\/span><\/p>\n 15. [latex]3|5-x|=5[\/latex]<\/span><\/p>\n 16.\u00a0[latex]3|x+1|-4=5[\/latex]<\/span><\/p>\n 17. [latex]5|x - 4|-7=2[\/latex]<\/span><\/p>\n 18.\u00a0[latex]0=-|x - 3|+2[\/latex]<\/span><\/p>\n 19. [latex]2|x - 3|+1=2[\/latex]<\/span><\/p>\n 20.\u00a0[latex]|3x - 2|=7[\/latex]<\/span><\/p>\n 21. [latex]|3x - 2|=-7[\/latex]<\/span><\/p>\n 22.\u00a0[latex]\\left|\\frac{1}{2}x - 5\\right|=11[\/latex]<\/span><\/p>\n 23. [latex]\\left|\\frac{1}{3}x+5\\right|=14[\/latex]<\/span><\/p>\n 24.\u00a0[latex]-\\left|\\frac{1}{3}x+5\\right|+14=0[\/latex]<\/span><\/p>\n For the following exercises, find the x- and y-intercepts of the graphs of each function.<\/span><\/p>\n 25. [latex]f\\left(x\\right)=2|x+1|-10[\/latex]<\/span><\/p>\n 26.\u00a0[latex]f\\left(x\\right)=4|x - 3|+4[\/latex]<\/span><\/p>\n 27. [latex]f\\left(x\\right)=-3|x - 2|-1[\/latex]<\/span><\/p>\n 28.\u00a0[latex]f\\left(x\\right)=-2|x+1|+6[\/latex]<\/span><\/p>\n For the following exercises, solve each inequality and write the solution in interval notation.<\/span><\/p>\n 29. [latex]\\left|x - 2\\right|>10[\/latex]<\/span><\/p>\n 30.\u00a0[latex]2|v - 7|-4\\ge 42[\/latex]<\/span><\/p>\n 31. [latex]|3x - 4|\\le 8[\/latex]<\/span><\/p>\n 32.\u00a0[latex]|x - 4|\\ge 8[\/latex]<\/span><\/p>\n 33. [latex]|3x - 5|\\ge 13[\/latex]<\/span><\/p>\n 34.\u00a0[latex]|3x - 5|\\ge -13[\/latex]<\/span><\/p>\n 35. [latex]\\left|\\frac{3}{4}x - 5\\right|\\ge 7[\/latex]<\/span><\/p>\n 36.\u00a0[latex]\\left|\\frac{3}{4}x - 5\\right|+1\\le 16[\/latex]<\/span><\/p>\n For the following exercises, graph the absolute value function. Plot at least five points by hand for each graph.<\/span><\/p>\n 37. [latex]y=|x - 1|[\/latex]<\/span><\/p>\n 38.\u00a0[latex]y=|x+1|[\/latex]<\/span><\/p>\n 39. [latex]y=|x|+1[\/latex]<\/span><\/p>\n For the following exercises, graph the given functions by hand.<\/span><\/p>\n 40. [latex]y=|x|-2[\/latex]<\/span><\/p>\n 41. [latex]y=-|x|[\/latex]<\/span><\/p>\n 42. [latex]y=-|x|-2[\/latex]<\/span><\/p>\n 43. [latex]y=-|x - 3|-2[\/latex]<\/span><\/p>\n 44.\u00a0[latex]f\\left(x\\right)=-|x - 1|-2[\/latex]<\/span><\/p>\n 45. [latex]f\\left(x\\right)=-|x+3|+4[\/latex]<\/span><\/p>\n 46. [latex]f\\left(x\\right)=2|x+3|+1[\/latex]<\/span><\/p>\n 47. [latex]f\\left(x\\right)=3|x - 2|+3[\/latex]<\/span><\/p>\n 48.\u00a0[latex]f\\left(x\\right)=|2x - 4|-3[\/latex]<\/span><\/p>\n 49. [latex]f\\left(x\\right)=|3x+9|+2[\/latex]<\/span><\/p>\n 50.\u00a0[latex]f\\left(x\\right)=-|x - 1|-3[\/latex]<\/span><\/p>\n 51. [latex]f\\left(x\\right)=-|x+4|-3[\/latex]<\/span><\/p>\n 52.\u00a0[latex]f\\left(x\\right)=\\frac{1}{2}\\left|x+4\\right|-3[\/latex]<\/span><\/p>\n 53.\u00a0Use a graphing utility to graph [latex]f\\left(x\\right)=10|x - 2|[\/latex] on the viewing window [latex]\\left[0,4\\right][\/latex]. Identify the corresponding range. Show the graph.<\/span><\/p>\n 54.\u00a0Use a graphing utility to graph [latex]f\\left(x\\right)=-100|x|+100[\/latex] on the viewing window [latex]\\left[-5,5\\right][\/latex]. Identify the corresponding range. Show the graph.<\/span><\/p>\n For the following exercises, graph each function using a graphing utility. Specify the viewing window.<\/span><\/p>\n 55. [latex]f\\left(x\\right)=\\left(-0.1\\right)\\left|0.1\\left(0.2-x\\right)\\right|+0.3[\/latex]<\/span><\/p>\n 56.\u00a0[latex]f\\left(x\\right)=4\\times {10}^{9}\\left|x-\\left(5\\times {10}^{9}\\right)\\right|+2\\times {10}^{9}[\/latex]<\/span><\/p>\n For the following exercises, solve the inequality.<\/span><\/p>\n 57. [latex]\\left|-2x-\\frac{2}{3}\\left(x+1\\right)\\right|+3>-1[\/latex]<\/span><\/p>\n 58.\u00a0If possible, find all values of [latex]a[\/latex] such that there are no [latex]x\\text{-}[\/latex] intercepts for [latex]f\\left(x\\right)=2|x+1|+a[\/latex].<\/span><\/p>\n 59. If possible, find all values of [latex]a[\/latex] such that there are no [latex]y[\/latex] -intercepts for [latex]f\\left(x\\right)=2|x+1|+a[\/latex].<\/span><\/p>\n 60.\u00a0Cities A and B are on the same east-west line. Assume that city A is located at the origin. If the distance from city A to city B is at least 100 miles and [latex]x[\/latex] represents the distance from city B to city A, express this using absolute value notation.<\/span><\/p>\n 61. The true proportion [latex]p[\/latex] of people who give a favorable rating to Congress is 8% with a margin of error of 1.5%. Describe this statement using an absolute value equation.<\/span><\/p>\n 62.\u00a0Students who score within 18 points of the number 82 will pass a particular test. Write this statement using absolute value notation and use the variable [latex]x[\/latex] for the score.<\/span><\/p>\n 63. A machinist must produce a bearing that is within 0.01 inches of the correct diameter of 5.0 inches. Using [latex]x[\/latex] as the diameter of the bearing, write this statement using absolute value notation.<\/span><\/p>\n 64.\u00a0The tolerance for a ball bearing is 0.01. If the true diameter of the bearing is to be 2.0 inches and the measured value of the diameter is [latex]x[\/latex] inches, express the tolerance using absolute value notation.<\/span><\/p>\n\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t