anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
@Thesn1 can you please help I tried googling it and I cant find it
anonymous
  • anonymous
@jim_thompson5910 hey can you help?

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

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