Question

The graph below shows a company's profit f(x), in dollars, depending on the price of pencils x, in dollars, being sold by the company:

Part B: If at one time the profit of the company was at least $100, 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 = 5, and what does this rate represent?

I have attached the graph below.

Answer 1

For Part B, it appears that the domain would be x => 2, x<=9.7.

Answer 2

Is this correct?

@triciaal @sleepyjess @mathmale @mathstudent55 @mathmate @zepdrix @ganeshie8 @ParthKohli @pooja195

Answer 3

do you have the function for the graph?
what exactly is f(x)?

Answer 4

Where did you get 9.7?

Answer 5

x => looks to be correct.

Answer 6

*x=>2 I mean

Answer 7

For C, do you know the formula for average rate of change (or slope)?

Answer 8

@epistemeal No I don't.

And for

Answer 9

Question B, if you look at the question is says If at one time the profit of the company was at least $100, what domain could possibly produce this profit?

Answer 10

It says at least 100$.

I got the 9.7, because if you look at the graph

Answer 11

The right side of the graph starts to go down, around 9.7 is the place where it reaches 100 on the right side of the graph. I assumed they wanted to know both sides

Answer 12

Alright. This is something you'll need to keep. it's \[(y_2 - y_1)\div(x_2-x_1)\]. Or rise (change in y) over run (change in x)

Answer 13

You have the right idea, but it looks more like 8 for me.

Answer 14

So can you get the average rate of change now?

Answer 15

@epistemeal I know the Rise over Run thing, but does that apply to a line that is curved?

Answer 16

Oh and what should the domain be? x => 2, x<=8?

Answer 17

It should for *average* rate of change.

And yes, that looks right. good job

Answer 18

Alright, Part C: What is an approximate average rate of change of the graph from x = 2 to x = 5, and what does this rate represent?

Answer 19

So the coordinates for x = 2 and x = 5 are

Answer 20

(2, 100) and (5, 160)

Answer 21

Equation:

(y2−y1)÷(x2−x1)

Answer 22

y2 = 160, y1 = 100

x2 = 5, x = 2

@epistemeal ?

Answer 23

So that would be

Answer 24

\[\frac{ 160 - 100 }{ 5 - 2 } = \frac{ 60 }{ 3 } = \frac{ 20 }{ }\]

Answer 25

@epistemeal ????????

Answer 26

So would the average rate of change be 20?

Answer 27

Oh, the last fraction is missing a 1 in the denominator

Answer 28

That looks perfectly correct. Nice

Answer 29

Yeah I got it.

Answer 30

So the average rate of change would be about 20, correct?

Answer 31

Yes

Answer 32

And the domain is x => 2, x<=8, correct?

Answer 33

Yes

Answer 34

Alright, Thanks again @epistemeal !

Answer 35

No problem!

Answer 36

Bye!

Answer 37

If you're satisfied, could you click the little "best response" button on one of my responses?

Answer 38

Already did. :)

g2g!

Answer 39

oh ok. See ya!