Question

Help me please! Algebra 1 question, I really really need help. Medal if any help is given at all!

Answer 1

The graph below shows a company's profit f(x), in dollars, depending on the price of pens 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? (5 points)

Part B: If at one time the profit of the company was at least sixty dollars, what domain could possibly produce this profit? (2 points)

Part C: What is an approximate average rate of change of the graph from x = 3 to x = 5 and what does this rate represent? (3 points)

Answer 2

please help me :(

Answer 3

@kirbykirby can you help?

Answer 4

A) the x-intercept is when f(x) = 0. We know f(x) is the profit, so the x-intercept means he is getting no profit when x=0 and x=6 (and x is the price of pens.. so obviously is the price of a pen is 0, he is not making profit, and if the price is 6, he isn't making profit either)... So the price of the pen is probably too expensive and not enough people are buying it at that price so that he can make a profit.

The function is increasing on \(x\in(-\infty,3]\) and decreasing on \(x\in[3,+\infty)\) since 3 is the maximum point.

On the increasing part of the graph: he is continually making more and more profit until he reaches the highest profit attainable at x=3 where his profit is $120.

Then on the decreasing portion of the graph, his profit declines gradually with increasing pen price (x).

Why isn't he making more money as the price increases all the time (this is relating to the sales of the pens)? Well I alluded to that in my first paragraph. There's an economic factor of supply/demand here. On the increasing portion of the graph, people may be fairly "indifferent" about paying for a pen for less than 3 dollars, but his max is reached at 3 since it's a higher price. But after 3 dollars, people are less willing to buy pens because they are too expensive. And it turns out that not enough people are willing to buy the pens at a price greater than 3 for him to make larger profits. But you have to realize that there are other costs. Like if the merchant buys a box of 5 pens, but he only sells 2 of them at a price of 5.75, then he will not make a large profit (of course, depending on the price of the box of pens).

Answer 5

B: Just look where the y-axis cuts at 60$. The curve part above 60 is telling you the part of the graph where the profit is larger than 60. So, the corresponding domain for this is \(x\in[1,5]\) (look at the x-axis where the y-value of 60 occurs).

Answer 6

C: average rate of change... just think of it as a line crossing the points at x=3 and x=5.

The coordinates for these points are (3, 120) and (5, 60). So the average rate of change is \[\frac{\Delta y}{\Delta x} =\frac{120-60}{3-5}=-30\]. So the average rate is negative, which means that on average, the profits decrease by $30 per increase in $1 in pen price.