Question

You are having a meeting with the CEO of a soda company. You have interpreted the number of cans of soda produced versus profit as the function P(x) = x4 + 2x3 + 6x2 - 3x - 7. Describe to the CEO what the graph looks like. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0).
@satellite73 I need your help plz :)

Answer 1

really?
here is the graph
http://www.wolframalpha.com/input/?i=+x4+%2B+2x3+%2B+6x2+-+3x+-+7

Answer 2

you sure you didn't make a typo there right? the zeros are impossible to find without technology here

Answer 3

for the "end behavior" you see that as \(x\to \infty\) you have \(p(x)\to \infty\)

Answer 4

in other words, the more cans of soda you make the more money you make

Answer 5

i'm sure it isn't a typo i copied it word for word

Answer 6

since you cannot make negative cans of soda, we should restrict the domain of this function to \(x>0\)

Answer 7

it looks ilke the graph crosses the x axis at just less than \(x=1\) so if you make only one can of soda you still make a profit

Answer 8

okay I'll send you my answer and please tell me if its right or not

Answer 9

can u fan me so i cand send u an inbox of my answer?

Answer 10

this is an amazingly idiotic question
if you make only 10 cans of soda your profit is \[p(10)=\$12,563\]

Answer 11

i really need help im stuckk :/ I dont know what to doo!

Answer 12

ok

Answer 13

lets go slow and do what it asks you to do

Answer 14

\[P(x) = x^4 + 2x^3 + 6x^2 - 3x - 7 \] is supposed to be your profit on \(x\) cans of soda

Answer 15

right

Answer 16

Describe to the CEO what the graph looks like
for values of \(x\) that are greater than zero, the graph grows very quickly

Answer 17

i will send you a picture
it almost looks like a parabola, but not quite
http://www.wolframalpha.com/input/?i=+x4+%2B+2x3+%2B+6x2+-+3x+-+7+domain+0..10

Answer 18

you can see that if you make only ten cans of soda you make over \(\$12,000\)
i didn't write this question, i call them as i see them

Answer 19

the end behaviour: the more cans of soda you make, the bigger your profit

Answer 20

where the company will break even (where P(x) = 0)
for this one \(p(x)=0\) for \(x\) just about 1, which means if you make one can of soda you will make a profit

Answer 21

no point in asking again if you copied this correctly, i believe you but it is rather silly
i wish i could make this kind of money

Answer 22

there is not really anything else to say
i did fan you if you need to send me a message

Answer 23

okay thanks

Answer 24

is that answer complete enough for you? not sure what else to say

Answer 25

its kind of confusing for me its really hard to understand they always give us these really dumb question that we've never even went through during class and just expect you to know whatever they give u out of the blues.

Answer 26

ok your answer makes sense in terms of the graph, but no in terms of the question
the question has x as the number of cans of soda made
you can't really make negative cans of soda

Answer 27

but you are doing the best you can for the tools that you got, so go ahead with your answer
you also are supposed to say what the "end behaviour" is, so include the fact that the more cans of soda you make, the more money you make

Answer 28

can u help me out by adding that cuz i have no idea what else to say if you don't want to i understand :)

Answer 29

just say what i just wrote
as \(x\to \infty, p(x)\to \infty\) so the more cans of soda you make, the higher your profit
you can copy that verbatim

Answer 30

that should be good enough

Answer 31

thank you so much i appreciate it! :)

Answer 32

i have one more i'm stuck on

Answer 33

lets get to it then

Answer 34

thankss :)

Answer 35

Your friend hands you a graph of the engine power statistics of a race car. He says, “I know this graph is f(x) = –3(x + 4)6 – 8 but I can’t remember how it is related to the graph of x6.” Explain to your friend how the graph f(x) is a translation of the graph x6.

Answer 36

dreaded question marks again
let me refresh

Answer 37

ok

Answer 38

\[f(x)=-3(x+4)^6-8\]

Answer 39

how does this translate from \[y=x^6\]

Answer 40

1) from \(y=x^6\) to \(y=(x+4)^6\) the graph shifts 4 units to the LEFT
(write these down)

Answer 41

okay :) @satellite73

Answer 42

2) from \(y=(x+4)^6\) to \(y=-3(x+4)^6\) the graph rotates (flips) about the \(x\) axis and becomes narrower by a factor of 3

Answer 43

3) from \(y=-3(x+4)^6\) to \(y=-3(x+4)^6-8\) the graph shifts DOWN 8 units

Answer 44

got it :)

Answer 45

here is the graph on the interval \((-4,2)\)
http://www.wolframalpha.com/input/?i=-3%28x%2B4%29^x-8+domain+-4..2

Answer 46

alright @satellite73

Answer 47

hope you are done