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 x^4.” Explain to your friend how the graph f(x) is a translation of the graph x^4.
I get translations, but I can't seem to identify this one.

Question

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 x^4.” Explain to your friend how the graph f(x) is a translation of the graph x^4.
I get translations, but I can't seem to identify this one.

anonymous · Answer

i hope there is a typo there

anonymous · Answer

$$ f(x) = –3(x + 4)^6 – 8$$ should maybe be 
$$ f(x) = –3(x + 4)^4 – 8$$

anonymous · Answer

it is shifted a few ways

anonymous · Answer

4 units to the left
flipped about the $x$ axis because of the $-3$
then down $8$ units because of the $-8$ 
also narrower because of the $x^6$

anonymous · Answer

it is the minus sign that flips it over the $x$ axis

anonymous · Answer

compare say $y=x^2$ to $y=-x^2$

anonymous · Answer

and $x^6$ is narrow than $x^4$ because raising a number to the power of 6 makes it a lot bigger than raising it to the power of 4 (assuming it is larger than 1)

anonymous · Answer

yes

anonymous · Answer

i mean yes the $x+4$ shifts it 4 units left

anonymous · Answer

sure what is the other one ?

anonymous · Answer

they really stretch to make these word problem, don't they?
"break even" they tell you just means $p(x)=0$ so you have to find the zeros of this thing
your first answer is correct. 
lets find the zeros

anonymous · Answer

yes stay graphical
the zeros are not rational

anonymous · Answer

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

anonymous · Answer

well really it would not have domain $\mathbb{R}$ but rather $(0,\infty)$ since you do not make a negative amount of cans

anonymous · Answer

yes