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?

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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?

Algebra
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1 Attachment
@Thesn1 can you please help I tried googling it and I cant find it
@jim_thompson5910 hey can you help?

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how far did you get with this? did you get started at all?
you want solution of all this or just the last question ??
@jim_thompson5910 no I didn't start im confused with this topic
what does x represent (this is given at the top) ?
x is price of notebooks
how about f(x) ?
company's profit
correct
the x-intercepts are when f(x) = 0 so what does f(x) = 0 mean?
that the company started at $0?
not really "started" but just whenever the profit is $0 since f(x) = profit
oh ok. so for part a the x intercepts are 0 and 4 right?
correct, so what does that mean?
ummmmmm. idk?
when x = 0, the value of f(x) = 0 so when the price is $0, the profit is $0, agreed?
ya agree. so What do the x-intercepts and maximum value of the graph represent?
what does the x intercept of 4 represent?
the profit is $4?
not quite
then idk. im not good at quadratics
when the price is $4, the profit is $0
oh ok. so the x-intercepts are 0 and 4, and maximum value of the graph represent what?
when they say "max value" they mean the max value of f(x) how big can f(x) get?
300.
yep so that is the max profit because again, f(x) is the profit
what value of x corresponds to the max profit?
ok and 2.
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
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?
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
|dw:1433120212372:dw|
|dw:1433120219258:dw|
|dw:1433120232720:dw|
ok so what would I put for part a answer?
for the increasing/decreasing part, they just want the intervals along the x axis
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)
i don't get it. @jim_thompson5910
where are you stuck at
i just don't understand what you just said for the intervals.
do you see how on my example graph, the curve goes uphill as you go from left to right until you hit x = 10?
ya
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
oh ok so for my graph, it would be 0
for increasing. and then i don't know about decreasing
actually 0 < x < 2 look along the x axis (not y)
ohhhhhh. so what would the decreasing be?
give it a shot
hopefully you see how I'm getting 0 < x < 2 ?
2
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
notice how with the increasing part, I ignored everything to the left of x = 0
ya. ok so i just have to look at the x axis right? when i do this
yeah whenever looking at intervals of decreasing or increasing
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
Simply state in your own words the things we went over the roots, the max, the increasing/decreasing intervals
but itt also says what does it represent and idk what to put for that
Part B: At one time the profit of the company was at least $220, what domain could possibly produce this profit? @jim_thompson5910
@jim_thompson5910 can you help me with part b and c!!??
draw a horizontal line through y = 220 where does this horizontal line cross the parabola? at what two points?
how do i do that?
1 Attachment
ok so (1,220) and (3,220)
yes
so the profit is at least $220 when x is between 1 and 3 (inclusive) \[\Large 1 \le x \le 3\]
if the company wants a profit of $220 or greater, then it needs to have the price between $1 and $3
ok so that would be my answer?
yeah the domain is another way of asking for an interval
do you see how to do part C?
um no i need help with this sorry
what are the two points on the parabola when x = 2 and x = 4?
x= 2 is 300? and x=4 0?
yep so we have the two points (2,300) and (4,0)
what is the slope of the line through those two points?
would it be a decreasing line
yes the slope is some negative number
ok so what would my answer be, A negative line that goes through 2,300 and 4,0
use the slope formula \[\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]
what slope do you get?
um one second let me solve it
-150
correct
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)
ok so -150 is the approximate average rate of change. and this rate represents what? so i put that down?
yeah in your own words of course
ya ik that. thanks so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
you're welcome

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