A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ineedhelp10

  • one year ago

Erin buys gas at a self service station for $2.75 a gallon. The gas station has a promotion going on that anyone who buys more than 10 gallons of gas, only has to pay $2.50 per gallon. Erin's tank will hold 12 gallons of gas. a) Write a rule for the total cost, C(g), as a function of g gallons of gas. b)Graph the piecewise function c)What is the domain and range of the function in part a

  • This Question is Closed
  1. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @jim_thompson5910 help please

  2. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what do you have so far?

  3. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @jim_thompson5910 not much sir, i'm confused actually

  4. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    `Erin buys gas at a self service station for $2.75 a gallon` if Erin buys g gallons of gas, then how much does she spend?

  5. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how many gallons does Erin buy though?

  6. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok let's say she buys 5 gallons how much does she spend?

  7. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it'll be $13.75 then

  8. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how did you compute that

  9. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    by multiplying the number of gallons Erin was going to buy with the price that each gallon costs

  10. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so in general, we can say `2.75*g` or just `2.75g`

  11. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    g is it the unknown number of gallons bought

  12. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay yeah i understand that

  13. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If the promotion wasn't there, then C(g) = 2.75g and that would be it. There wouldn't be a need for a piecewise function

  14. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    however, the promotion changes things C(g) = 2.75g is only true if \(\Large 0 \le g \le 10\) anything larger than 10 will have a different price structure

  15. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so it wouldn't be just greater than? it's greater than or equal to right

  16. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so that'll be the rule for letter a?

  17. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    not the full rule

  18. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh okay so then what else do we need?

  19. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    `The gas station has a promotion going on that anyone who buys more than 10 gallons of gas, only has to pay $2.50 per gallon.` what is the cost function if you buy more than 10 gallons of gas?

  20. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i seriously dont know D:

  21. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    same as before total cost = (price per gallon)*(number of gallons) keep the number of gallons as g the price will change

  22. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    C(g)=2.50g

  23. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what are the restrictions on g?

  24. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you pay $2.50 per gallon if you bought say, 8 gallons?

  25. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no, it's when you buy more than 10 gallons so wouldn't it be \[0\le g \le 10\]

  26. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    more like g > 10 if g > 10, then the cost function is C(g) = 2.50g

  27. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now let's form the piecewise function

  28. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Everything in blue \[\Large \color{blue}{ \Large C(g) = 2.75g \text{ if } 0 \le g \le 10 \\ \Large \text{OR}\\ \Large C(g) = 2.50g \text{ if } g > 10 \\ }\] condenses to this piecewise function notation you see in red \[\Large \color{red}{C(g)=\begin{cases}2.75g \text{ if } 0 \le g \le 10 \\ 2.50g \text{ if } g > 10 \end{cases}}\] The stuff in red is what most math books will use as piecewise function notation. The stuff in blue is more intuitive (at least to me), so it's good to know both forms.

  29. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    take a few moments to write down notes and process all this. I want to make sure you understand all this before we move on

  30. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ah okay i see what you did there, so basically what's in blue is the rule for the total cost correct?

  31. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and then what's in red is basically the rule for the total cost but more "like what textbooks would use" right

  32. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah the cost function is either one or the other (pick one) and it's based on what g is if g is between 0 and 10, you pick the first one if g is greater than 10, you pick the second one

  33. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    correct, it's the formal mathematical way

  34. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ah okay this is making so much more sense now, okay im done taking notes now

  35. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    once you get to the red stuff, you are done with part a)

  36. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ready for part b)?

  37. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah

  38. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    to graph a piecewise function, we simply graph each piece on the same xy axis so focus on just the first piece C(g) = 2.75g do you know how to graph that?

  39. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    tbh no i dont how will you start it?

  40. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    think of it as y = 2.75x

  41. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what kind of equation is that?

  42. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hint: y = mx+b

  43. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it's slope intercept form right?

  44. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah we have slope m = 2.75 and y intercept b = 0 do you see how I'm getting that?

  45. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i see how plus i just graphed it on my calculator and it gave me the coordinates to graph.

  46. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what two points are on this graph

  47. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    two points are (1,2.75) and (2,5.5)

  48. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    good

  49. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and then the second one will be y=2.50x ?

  50. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so normally, when you graph y = 2.75x, you draw a straight line through those two points

  51. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    however, there's a restriction on x in this case, \(\Large 0 \le x \le 10\) is the restriction

  52. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so does that mean stop graphing when the x coordinate is at 10?

  53. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so what that means is that you only graph the portion between x = 0 and x = 10 you erase everything else

  54. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1442368336119:dw|

  55. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1442368346952:dw|

  56. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1442368378189:dw|

  57. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    make sense?

  58. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah it makes sense

  59. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and how will that be different for c(g)=2.50g

  60. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now we plot closed circles at the endpoints because we are including the endpoints |dw:1442368517079:dw|

  61. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    then we move onto graphing y = 2.50x this is only graphed when x > 10

  62. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so how will that one look? that one looks more confusing

  63. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so graph y = 2.50x like normal then erase the portion to the left of x = 10

  64. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wait you think you can draw an example of it please?

  65. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what two points are on y = 2.50x

  66. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (1,2.5) and (2.5)

  67. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    (2,5) you mean?

  68. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah lol sorry that's what i meant

  69. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    plot the two points, draw a line through them that will get you the graph of y = 2.50x

  70. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    then erase the portion to the left of x = 10

  71. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that's whats confusing me when you say left of x=10 like where on the graph is that ?

  72. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1442368737285:dw|

  73. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1442368751023:dw|

  74. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1442368771771:dw|

  75. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1442368802811:dw|

  76. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ah okay so then the first point wouldn't be (10,25) right?

  77. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you'll have this left over |dw:1442368832183:dw|

  78. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  79. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    there is an open circle at (10,25) because it is NOT included this is because there is no line under the `>` in `g > 10` |dw:1442368915013:dw|

  80. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ah okay i get the graphing now

  81. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    let's put the two pieces together to form one single graph |dw:1442368938829:dw|

  82. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    here's what desmos shows https://www.desmos.com/calculator/oyvslmmg3f so it confirms things. The only thing missing is the open & closed circles at the endpoints

  83. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ah okay sounds good so far

  84. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what about the domain and range of the function in part a?

  85. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    tell me what you think the domain would be

  86. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    will the domain be anything greater than or equal to 10? :///

  87. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no wait would it be 12 since that's how many gallons erin can hold in his car?

  88. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you're forgetting the stuff lower than 10

  89. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can you explain the domain please

  90. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you're right, she can only hold 12 gallons of gas so the domain would be the set of numbers between 0 and 12 the domain is the set of allowed numbers of gallons of gas that can be bought (in this specific case, just for Erin)

  91. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so it'll be \[x \le 12\]

  92. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    actually \[\Large 0 \le g \le 12\]

  93. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and what about the range? i always had trouble with range

  94. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @jim_thompson5910 are you there still?

  95. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry I went away from my computer for a moment

  96. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you see how I got that domain?

  97. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i saw how now

  98. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im just confused on the range now

  99. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what is the smallest value in the domain?

  100. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    0

  101. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    plug that into C(g) to get ??

  102. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    0 again

  103. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so 0 is the smallest number in the range

  104. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what is the largest number in the domain?

  105. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its 12

  106. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    if g = 12, then C(g) = ??

  107. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    $30 ?

  108. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so the range spans from 0 to 30 (including both endpoints)

  109. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how will that look like when writing it down?

  110. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    well you can either say \[\Large 0 \le y \le 30\] or \[\Large 0 \le C(g) \le 30\]

  111. ineedhelp10
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ah okay i get it now thanks soooooooooo much!! i really appreciate you taking time to help me out on this problem i appreciate it!

  112. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm glad to be of help

  113. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.