29. It is discrete because you cant have a part of a marble, only a whole marble
30. This is continuous because you can have a portion of a year.
31. This is continuous because time can be broken down into smaller intervals
32. This is discrete because you cant have a part of a team. x values between the given ones would give you a fraction of a team.
33. In this graph, the line is not continuous. Therefore, because there is no point at 2.5, 2.5 is not in the domain.
34. Even though the graph ends at x=6, all possible values of x between 0-6 are accounted for, making the line continuous. So, the line is continuous.
35. a. To find the domain, we have to solve for b first by making m=0. So, 0=55-8.5b -55 = -8.5b, which is 55/8.5, or 110/17 So, the domain is 0<=x<=(110/117) This is a discrete line because you can only have whole numbers for "b" because you can only buy whole books b.(cant really graph it on here :P ) c. When x = 0, y = 55, and when x = 110/117, y = 0. So the range is 0<=y<=55
36. a. Because there is no limit to the function, the domain is x>=0. The function is continuous because the time can be broken down into smaller intervals b. (cant really graph it on here :P ) c. The range is y>=0 because the least x can be is 0, but it can keep increasing.
37. a. This does represent a linear function because the distance increases by .434 miles at every interval (every 2 seconds) b. The domain would be t>=0 because you can't have negative time, but you can wait infinitely long. This should be continuous because time and distance can be broken down into smaller intervals. c. (cant really graph it on here :P ) d. The smallest t can be is 0, and when t=0, d=0. Because domain is infinite, range is also infinite. Therefore the range is d>=0
38. a. It is linear because there is an 'x' input and 'y' output and there are no exponents in either variable. b. x can equal 0, and it can be infinite. So, the domain is x>=0. It is discrete because you cant have a partial service, only a whole. c. (cant really graph it on here :P ) d. When x=0, y=30. Because domain is infinite, range is also infinite. Therefore the range is y>=30
43. a. If you subtract 61.20 from 71.40, you can see that every hour, the earnings increase by 10.20 dollars. Therefore, the missing value is 61.20-10.20, or 51.00 b. Every hour you get 10.20.
44. a. This is not a linear function. This is because the function breaks at t=5, which should be 300 if it was following the original pattern, which was d=60t When t=1, d=60 When t=3, d=180. But, when t=5, in the function, it equals 300 while in actuality, it equals 300 b. He is correct because if Car A is still following the function, it would have only gone 300 miles, while Car B had gone 310 miles.
Hope this helped!! Let me know if any of this is unclear or if you're still having some trouble!! :D
Linear equations are straight lines while quadratics are curved in a "u" shape. These points have a vertex and go up on both sides, a quadratic would be able to better fit this since their y values repeat, unlike linear models.
