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@jim_thompson5910 help please

what do you have so far?

@jim_thompson5910 not much sir, i'm confused actually

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how many gallons does Erin buy though?

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

it'll be $13.75 then

how did you compute that

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

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

g is it the unknown number of gallons bought

okay yeah i understand that

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

so that'll be the rule for letter a?

not the full rule

oh okay so then what else do we need?

i seriously dont know D:

C(g)=2.50g

what are the restrictions on g?

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

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

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

now let's form the piecewise function

correct, it's the formal mathematical way

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

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

ready for part b)?

yeah

tbh no i dont how will you start it?

think of it as y = 2.75x

what kind of equation is that?

hint: y = mx+b

it's slope intercept form right?

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

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

what two points are on this graph

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

good

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

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

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

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

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|dw:1442368346952:dw|

|dw:1442368378189:dw|

make sense?

yeah it makes sense

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

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

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

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

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

what two points are on y = 2.50x

(1,2.5) and (2.5)

(2,5) you mean?

yeah lol sorry that's what i meant

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

then erase the portion to the left of x = 10

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

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|dw:1442368751023:dw|

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

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

yes

ah okay i get the graphing now

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

ah okay sounds good so far

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

tell me what you think the domain would be

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

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

you're forgetting the stuff lower than 10

can you explain the domain please

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

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

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

@jim_thompson5910 are you there still?

sorry I went away from my computer for a moment

do you see how I got that domain?

yeah i saw how now

im just confused on the range now

what is the smallest value in the domain?

plug that into C(g) to get ??

0 again

so 0 is the smallest number in the range

what is the largest number in the domain?

its 12

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

$30 ?

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

how will that look like when writing it down?

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

I'm glad to be of help

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