Please help!
The graph below shows a company's profit f(x), in dollars, depending on the price of notebooks x, in dollars, being sold by the company:
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?
Part B: At one time the profit of the company was at least $220, what domain could possibly produce this profit?
Part C: What is an approximate average rate of change of the graph from x = 2 to x = 4, and what does this rate represent?

- anonymous

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- anonymous

##### 1 Attachment

- anonymous

@Thesn1 can you please help I tried googling it and I cant find it

- anonymous

@jim_thompson5910 hey can you help?

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## More answers

- jim_thompson5910

how far did you get with this? did you get started at all?

- anonymous

you want solution of all this or just the last question ??

- anonymous

@jim_thompson5910 no I didn't start im confused with this topic

- jim_thompson5910

what does x represent (this is given at the top) ?

- anonymous

x is price of notebooks

- jim_thompson5910

how about f(x) ?

- anonymous

company's profit

- jim_thompson5910

correct

- jim_thompson5910

the x-intercepts are when f(x) = 0
so what does f(x) = 0 mean?

- anonymous

that the company started at $0?

- jim_thompson5910

not really "started" but just whenever the profit is $0
since f(x) = profit

- anonymous

oh ok. so for part a the x intercepts are 0 and 4 right?

- jim_thompson5910

correct, so what does that mean?

- anonymous

ummmmmm. idk?

- jim_thompson5910

when x = 0, the value of f(x) = 0
so when the price is $0, the profit is $0, agreed?

- anonymous

ya agree. so What do the x-intercepts and maximum value of the graph represent?

- jim_thompson5910

what does the x intercept of 4 represent?

- anonymous

the profit is $4?

- jim_thompson5910

not quite

- anonymous

then idk. im not good at quadratics

- jim_thompson5910

when the price is $4, the profit is $0

- anonymous

oh ok. so the x-intercepts are 0 and 4, and maximum value of the graph represent what?

- jim_thompson5910

when they say "max value" they mean the max value of f(x)
how big can f(x) get?

- anonymous

300.

- jim_thompson5910

yep so that is the max profit
because again, f(x) is the profit

- jim_thompson5910

what value of x corresponds to the max profit?

- anonymous

ok and 2.

- jim_thompson5910

yep so when x = 2, f(x) = 300
therefore, when the price is $2, the max profit is $300. This is where the company wants to aim

- anonymous

ok that makes more sense. ok and then for part a still What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?

- jim_thompson5910

the function is increasing if you are going uphill as you go from left to right
decreasing is the opposite way (downhill) as you go from left to right

- jim_thompson5910

|dw:1433120212372:dw|

- jim_thompson5910

|dw:1433120219258:dw|

- jim_thompson5910

|dw:1433120232720:dw|

- anonymous

ok so what would I put for part a answer?

- jim_thompson5910

for the increasing/decreasing part, they just want the intervals along the x axis

- jim_thompson5910

for example (this is not the answer, just an example)
say we had this scale
|dw:1433120434137:dw|
the increasing interval would be from x = 0 to x = 10
you can write that as 0 < x < 10 or in interval notation as (0,10)
the decreasing interval would be from x = 10 to x = 20
you can write that as 10 < x < 20 or in interval notation as (10,20)

- anonymous

i don't get it. @jim_thompson5910

- jim_thompson5910

where are you stuck at

- anonymous

i just don't understand what you just said for the intervals.

- jim_thompson5910

do you see how on my example graph, the curve goes uphill as you go from left to right until you hit x = 10?

- anonymous

ya

- jim_thompson5910

so that's how I got the interval from 0 to 10
0 < x < 10
basically when x is between 0 and 10, the graph is going uphill...ie increasing

- anonymous

oh ok so for my graph, it would be 0

- anonymous

for increasing. and then i don't know about decreasing

- jim_thompson5910

actually 0 < x < 2
look along the x axis (not y)

- anonymous

ohhhhhh. so what would the decreasing be?

- jim_thompson5910

give it a shot

- jim_thompson5910

hopefully you see how I'm getting 0 < x < 2 ?

- anonymous

2

- jim_thompson5910

that's a possibility, but to be really practical, the company only cares about when the profit is 0 or positive (ideally when it's positive)
so it would be from x = 2 to x = 4. Anything beyond x = 4 is territory the company doesn't want to go into
so that's why it's practical to say 2 < x < 4 is the interval in which the function is decreasing. In a practical context anyway

- jim_thompson5910

notice how with the increasing part, I ignored everything to the left of x = 0

- anonymous

ya. ok so i just have to look at the x axis right? when i do this

- jim_thompson5910

yeah whenever looking at intervals of decreasing or increasing

- anonymous

ok got it! thanks i do flvs and its hard to do algebra online. anyways, to answer the whole part of part a, how would i put it as

- jim_thompson5910

Simply state in your own words the things we went over
the roots, the max, the increasing/decreasing intervals

- anonymous

but itt also says what does it represent and idk what to put for that

- anonymous

Part B: At one time the profit of the company was at least $220, what domain could possibly produce this profit? @jim_thompson5910

- anonymous

@jim_thompson5910 can you help me with part b and c!!??

- jim_thompson5910

draw a horizontal line through y = 220
where does this horizontal line cross the parabola? at what two points?

- anonymous

how do i do that?

- jim_thompson5910

##### 1 Attachment

- anonymous

ok so (1,220) and (3,220)

- jim_thompson5910

yes

- jim_thompson5910

so the profit is at least $220 when x is between 1 and 3 (inclusive)
\[\Large 1 \le x \le 3\]

- jim_thompson5910

if the company wants a profit of $220 or greater, then it needs to have the price between $1 and $3

- anonymous

ok so that would be my answer?

- jim_thompson5910

yeah the domain is another way of asking for an interval

- jim_thompson5910

do you see how to do part C?

- anonymous

um no i need help with this sorry

- jim_thompson5910

what are the two points on the parabola when x = 2 and x = 4?

- anonymous

x= 2 is 300? and x=4 0?

- jim_thompson5910

yep so we have the two points (2,300) and (4,0)

- jim_thompson5910

what is the slope of the line through those two points?

- anonymous

would it be a decreasing line

- jim_thompson5910

yes the slope is some negative number

- anonymous

ok so what would my answer be, A negative line that goes through 2,300 and 4,0

- jim_thompson5910

use the slope formula
\[\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]

- jim_thompson5910

what slope do you get?

- anonymous

um one second let me solve it

- anonymous

-150

- jim_thompson5910

correct

- jim_thompson5910

so the average rate of change from x = 2 to x = 4 is -150
what does this mean? it means that the profit decreased by an average of $150 per increase of the price by $1 (ie each time the price went up $1, the profit dropped by $150)

- anonymous

ok so -150 is the approximate average rate of change. and this rate represents what? so i put that down?

- jim_thompson5910

yeah in your own words of course

- anonymous

ya ik that. thanks so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

- jim_thompson5910

you're welcome

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