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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
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

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ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 help please

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what do you have so far?

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 not much sir, i'm confused actually

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.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?

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0how many gallons does Erin buy though?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1ok let's say she buys 5 gallons how much does she spend?

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0it'll be $13.75 then

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1how did you compute that

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0by multiplying the number of gallons Erin was going to buy with the price that each gallon costs

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so in general, we can say `2.75*g` or just `2.75g`

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1g is it the unknown number of gallons bought

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0okay yeah i understand that

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1If 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

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1however, 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

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0so it wouldn't be just greater than? it's greater than or equal to right

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0so that'll be the rule for letter a?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1not the full rule

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0oh okay so then what else do we need?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.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?

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0i seriously dont know D:

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1same as before total cost = (price per gallon)*(number of gallons) keep the number of gallons as g the price will change

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what are the restrictions on g?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1do you pay $2.50 per gallon if you bought say, 8 gallons?

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0no, it's when you buy more than 10 gallons so wouldn't it be \[0\le g \le 10\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1more like g > 10 if g > 10, then the cost function is C(g) = 2.50g

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1now let's form the piecewise function

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1Everything 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.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1take a few moments to write down notes and process all this. I want to make sure you understand all this before we move on

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0ah okay i see what you did there, so basically what's in blue is the rule for the total cost correct?

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0and then what's in red is basically the rule for the total cost but more "like what textbooks would use" right

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah 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

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1correct, it's the formal mathematical way

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0ah okay this is making so much more sense now, okay im done taking notes now

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1once you get to the red stuff, you are done with part a)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1ready for part b)?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1to 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?

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0tbh no i dont how will you start it?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1think of it as y = 2.75x

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what kind of equation is that?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1hint: y = mx+b

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0it's slope intercept form right?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah we have slope m = 2.75 and y intercept b = 0 do you see how I'm getting that?

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0yeah i see how plus i just graphed it on my calculator and it gave me the coordinates to graph.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what two points are on this graph

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0two points are (1,2.75) and (2,5.5)

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0and then the second one will be y=2.50x ?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so normally, when you graph y = 2.75x, you draw a straight line through those two points

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1however, there's a restriction on x in this case, \(\Large 0 \le x \le 10\) is the restriction

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0so does that mean stop graphing when the x coordinate is at 10?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so what that means is that you only graph the portion between x = 0 and x = 10 you erase everything else

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442368336119:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442368346952:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442368378189:dw

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0yeah it makes sense

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0and how will that be different for c(g)=2.50g

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1now we plot closed circles at the endpoints because we are including the endpoints dw:1442368517079:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1then we move onto graphing y = 2.50x this is only graphed when x > 10

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0so how will that one look? that one looks more confusing

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so graph y = 2.50x like normal then erase the portion to the left of x = 10

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0wait you think you can draw an example of it please?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what two points are on y = 2.50x

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1(2,5) you mean?

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0yeah lol sorry that's what i meant

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1plot the two points, draw a line through them that will get you the graph of y = 2.50x

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1then erase the portion to the left of x = 10

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0that's whats confusing me when you say left of x=10 like where on the graph is that ?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442368737285:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442368751023:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442368771771:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442368802811:dw

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0ah okay so then the first point wouldn't be (10,25) right?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you'll have this left over dw:1442368832183:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1there 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

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0ah okay i get the graphing now

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1let's put the two pieces together to form one single graph dw:1442368938829:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1here'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

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0ah okay sounds good so far

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0what about the domain and range of the function in part a?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1tell me what you think the domain would be

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0will the domain be anything greater than or equal to 10? :///

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0no wait would it be 12 since that's how many gallons erin can hold in his car?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you're forgetting the stuff lower than 10

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0can you explain the domain please

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you'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)

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0so it'll be \[x \le 12\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1actually \[\Large 0 \le g \le 12\]

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0and what about the range? i always had trouble with range

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 are you there still?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1sorry I went away from my computer for a moment

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1do you see how I got that domain?

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0yeah i saw how now

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0im just confused on the range now

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what is the smallest value in the domain?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1plug that into C(g) to get ??

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so 0 is the smallest number in the range

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what is the largest number in the domain?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if g = 12, then C(g) = ??

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so the range spans from 0 to 30 (including both endpoints)

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0how will that look like when writing it down?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1well you can either say \[\Large 0 \le y \le 30\] or \[\Large 0 \le C(g) \le 30\]

ineedhelp10
 one year ago
Best ResponseYou've already chosen the best response.0ah okay i get it now thanks soooooooooo much!! i really appreciate you taking time to help me out on this problem i appreciate it!

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I'm glad to be of help
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