Question

How do you describe the end behavior of (x+3)^3

Answer 1

same behavior as z^3 but it has moved so our new "z" is (x+3)
(It has the same graphic as x^3=y but moved in the x axis by 3 to the left (the zero is in x=-3))

Answer 2

Omg I don't get it

Answer 3

So it's 3 to the left ?

Answer 4

okay... by the end behavior of (x+3)^3 you meant?

Answer 5

Yes

Answer 6

"The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity."
So you use the limit
\[\lim_{x \rightarrow \pm \inf } (x+3)^3 \]
Do you know how to solve that?

Answer 7

No not at all.

Answer 8

ahmm...well if you have and incredibly large number, you add 3 to it and you power it by 3, you'll get an even larger number, so, it will tend to positive infinity

Now if you have a negative incredibly large number, it will be the same BUT!

(-x)(-x)(-x)=- (x^3), so for the negative infinity, our function tends to...negative infinity

Do you understand now?

Answer 9

So negative infinity is the end behavior ?

Answer 10

you can write it like this
f(x)=(x+3)^3
if x->∞ then the end behavior goes to ∞
if x-> -∞ then the end behavior tends to -∞
(The end behavior is how the functions react to the largest numbers possible for x, to your left (negatives) and to your right, positive)

Answer 11

I don't get it at all

Answer 12

First, the definition of End behavior is
"The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity."

Try to explain it to me with your own words

Answer 13

What does infinity have to do with it. i never heard of infinity being in Algebra II

Answer 14

It's the "end behavior" 'cos it try to explain how the function "reacts" at the ends of the function, that implies, for polynomial functions -inf and inf.. because they're countinuous for the whole "R"