## anonymous one year ago If the range of the function f(x)= 5x − 3 is {-13, -8, -3, 12, 17}, what is its domain? I am confused with the 5x-3, can someone help?

1. anonymous

@iCake @ICanAwnserQuestions

2. anonymous

i do not know.

3. anonymous

@jim_thompson5910

4. jim_thompson5910

The range is the set of possible outputs. So it's saying that the set of possible outputs are -13, -8, -3, 12, 17

5. anonymous

yeah i get that what i dont get is the 5x-3

6. jim_thompson5910

it wants the corresponding inputs for each output so say the output is y = -13 that means y = 5x - 3 -13 = 5x - 3 -13+3 = 5x -10 = 5x 5x = -10 x = -10/5 x = -2 So if the output is y = -13, then the input is x = -2

7. jim_thompson5910

you will do this for the other outputs to get the domain

8. anonymous

oh now i get it thanks!!! :D

9. jim_thompson5910

you're welcome

10. anonymous

what did you get? i get -2,-1,0,1,2

11. anonymous

@jim_thompson5910

12. jim_thompson5910

let me check

13. jim_thompson5910

I don't agree with 1 or 2 but the "-2,-1,0" part is correct

14. anonymous

okay let me try it again

15. anonymous

i dont get it what i have to do with the y=-13 and x-2 @jim_thompson5910

16. jim_thompson5910

do you see how I plugged in y = -13 and solved to get x = -2 ?

17. anonymous

yeah but i dont undersand it that much

18. jim_thompson5910

well the idea is that if you plug in x =-2, you'll get y = -13 out they want you to think in reverse. If y = -8 is the output, then what must the input be?

19. anonymous

-1 ?

20. anonymous

i mean -4

21. jim_thompson5910

yep because y = 5x-3 y = 5*(-1) - 3 ... replace x with -1 y = -5 - 3 y = -8 so this shows how if x = -1 is plugged in, then y = -8 pops out

22. jim_thompson5910

I'll be right back

23. anonymous

okay

24. jim_thompson5910

I'm back

25. jim_thompson5910

So do you see how plugging in x = -1 gives y = -8?

26. anonymous

yes

27. jim_thompson5910

and if y = -3, then what must x be?

28. anonymous

2?

29. jim_thompson5910

let's check y = 5x-3 y = 5*2 - 3 ... replace x with 2 y = 10-3 y = 7 so if x = 2, then y = 7 but we want y = -3

30. anonymous

i get it! thank you! I have 4 questions more can you help me? its for a home test

31. jim_thompson5910

I can't help with tests

32. anonymous

its practically a homework and its the last 4 questions that i have trouble with :/

33. anonymous

@jim_thompson5910

34. jim_thompson5910

Ok I'll help with 2 of them if it's a hw. Which 2 are giving you the most trouble?

35. anonymous

widget wonder produce widgets. They have found that the cost,c(x), of making x widgets is a quadratic function in terms of x. The company also discovered that it cost $16 to produce 2 widgets,$18 to produce 4 widgets, and $48 to produce 10 widgets. Find the total cost of producing 6 widgets. 36. anonymous i am so bad at that kind of problems like the paraghrap @jim_thompson5910 37. jim_thompson5910 ok let me look through it 38. anonymous okay 39. jim_thompson5910 do you have a TI calculator (like a TI83 or TI84) ? 40. anonymous no :/ but cellphone work? or a scientific calculator? 41. jim_thompson5910 the cellphone won't work because we need to do quadratic interpolation 42. jim_thompson5910 let me find a calculator 43. anonymous okay thanks for your effort and your time ;) :D 44. jim_thompson5910 ok I found this page http://www.solvemymath.com/online_math_calculator/interpolation.php you will type in [2,16], [4,18], [10,48] and hit calculate. Tell me what comes up 45. anonymous 46. jim_thompson5910 I got that as well 47. jim_thompson5910 now you plug x = 6 into that function to get your final answer 48. anonymous thas what i dont get because it a big division 49. jim_thompson5910 $\Large f(x) = \frac{x^2-4x+36}{2}$ $\Large f(6) = \frac{6^2-4(6)+36}{2}$ $\Large f(6) = \frac{36-4(6)+36}{2}$ $\Large f(6) = \frac{36-24+36}{2}$ $\Large f(6) = \frac{12+36}{2}$ $\Large f(6) = \frac{48}{2}$ $\Large f(6) = 24$ 50. jim_thompson5910 So this means it costs$24 to make 6 widgets

51. anonymous

ohh okay so i always going to subsitute the x for its value

52. anonymous

and how do you get that list of numbers? like this one that you type [2,16], [4,18], [10,48] @jim_thompson5910

53. jim_thompson5910

Given: "The company also discovered that it cost $16 to produce 2 widgets,$18 to produce 4 widgets, and $48 to produce 10 widgets." "it cost$16 to produce 2 widgets" means x = 2 and y = 16 "$18 to produce 4 widgets" means x = 4 and y = 18 "$48 to produce 10 widgets" means x = 10 and y = 48

54. jim_thompson5910

all that means we know (2,16), (4, 18) and (10,48) all lie on this parabola

55. anonymous

and how you know which ones where on the same parentesis

56. jim_thompson5910

what do you mean?

57. anonymous

some of the numbers where in the same parenthesis

58. anonymous

oh nevermind i get it. thanks for your help! i have to go Thanks a lot!!

59. anonymous

@jim_thompson5910

60. jim_thompson5910

alright I'm glad it's making sense now