## rebelchick777 3 years ago I need some help please. Write a function rule to describe each statement... the cost in dollars of printing dollar bills when it costs 3.8cents to print a dollar bill. the amount of money you earn mowing lawns at \$15 per lawn. the profit you make selling flowers at \$1.50 each when each flower costs you \$.80

1. tjones89

it costs 3.8 cents to print 1 dollar its costs 2 times 3.8 cents to print two dollars it costs 3 times 3.8 cents to print 3 dollars you can see a pattern here right?

2. rebelchick777

yeah,but how do i write them as function rules?

3. tjones89

we use variables! there should be two of them; one will represent the number of dollars, lets call that x and the other will represent the cost to print them, lets call that y

4. rebelchick777

my teacher told me to write the functions as f(x)=...

5. tjones89

ok lets use f(x) instead of y so the cost to print, f(x), should equal the number of dollars, x, times 3.8 cents

6. rebelchick777

so f(x)=3.8x

7. tjones89

yes

8. rebelchick777

ok so then for the second one would it be... f(x)=\$15x

9. tjones89

yep

10. tjones89

but actually I made a mistake on the first one

11. rebelchick777

I d dont understand how to write the third one though.

12. tjones89

the function for the first part should give us the cost in dollars, with f(x) = 3.8x we'll end up with the number of cents

13. tjones89

so you just convert 3.8 cents into dollars which should be .038

14. rebelchick777

the profit you make selling flowers at \$1.50 each when each flower costs you \$.80

15. tjones89

what is the profit if I sell one flower?

16. rebelchick777

70 cents

17. tjones89

right.. and if i sell two flowers?

18. rebelchick777

a dollar and 40 cents

19. tjones89

which is the same as 2 times 70 cents right? if I sell 3 flowers the profit would be 3 times 70 cents and if I sell x flowers the profit will be x times 70 cents

20. rebelchick777

ok so... would the function be f(x)=.70x?

21. tjones89

yes! good job

22. rebelchick777

Thanks. Now i have another question i have this equation... f(x)=\$0.59x where x+number of pounds. if i had \$10 to buy that turkey how big a turkey could i buy?

23. tjones89

you have f(x) = \$0.59x which in words is, the cost of a turkey, f(x), is the number of pounds, x, times 59 cents

24. tjones89

so the cost of a turkey is a function of the number of pounds that it weighs, does that make sense so far?

25. rebelchick777

yeah. i was wondering where you d plug in the \$10.

26. tjones89

the ten dollars goes where dollars is represented in the equation

27. tjones89

x is pounds f(x) is dollars so the equation, when we put in 10 dollars, becomes \$10 = \$0.59x

28. tjones89

and by solving for x you will have found out how big a turkey you could by with 10 dollars

29. tjones89

does that make sense?

30. rebelchick777

16.95lb. is what i got. Yeah it does make sense.

31. rebelchick777

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32. rebelchick777

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33. rebelchick777

i dont see the rule for either of these. It says to write a function rule. By the way.. they are two seperate questions.

34. tjones89

ok lets start with the top one we need to find a way to relate x and y in other words we need to be able to describe how much y changes when x changes we can do this with a function y = x times (some number)

35. rebelchick777

i know that,but idk what number it should be.,

36. tjones89

we can find out what number it is by calculating the slope between the points that are given

37. tjones89

with m = (y2-y1)/(x2-x1)

38. rebelchick777

ok. so what should i get?

39. tjones89

lets use the points: (0,1) and (1,3) m = (3-1)/(1-0) = 2

40. rebelchick777

i understand it for the second table the answer would be f(x)=-4.5x. But i still dont see a pattern in the first one.

41. tjones89

maybe graphing the points and seeing them line up would help

42. rebelchick777

the y's are going up by two except for the last one.

43. tjones89

because its a negative x in the last one, if it were positive 3 then y would be 7

44. tjones89

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45. tjones89

thats the pattern if we follow the negative x points

46. tjones89

the reason it isnt as easy to see as the second problem is because this function will have the form y = mx + b

47. tjones89

whereas the second one was just y = mx

48. rebelchick777

ok so whats the function rule.

49. tjones89

well we're using y = mx + b as the template for our function, we found m to be 2, now we need to find b

50. tjones89

so we have y = 2x + b since we're given points we can substitute one in for the values of x and y, and then solve for b so if we use (0,1) as our point we get 1 = 2(0) + b so b = -1

51. tjones89

and keep in mind that we could have used any of the points that were given for example if we used (2,5) we get 5 = 2(2) +b and again b = -1

52. tjones89

so now that we know b, we can finally write the function as y = 2x -1

53. rebelchick777

thank you.

54. tjones89

np :)