Question

Which function has the flowing behavior? as x approaches ( i'll put the symbol in the comments), y approaches (symbol)
as x approaches (symbol), y approaches (symbol)

a y=x3-8x2-16
b y=x4-8x2+16
c y=-x4+8x2-16
d y= -x3-8x+16

Answer 1

Symbol is: \[-\infty -\infty \infty and -\infty\]

Answer 2

I put the symbols in order according the the question

Answer 3

So this is asking...as x approaches negative infinity, y approaches negative infinity AND as x approaches infinity, y approaches negative infinity

lets test them

a) y=x3-8x2-16

if we plug -infinity in here for x.....we also get -infinity for y (-infinity ^ 3 = -infinity)
check the other side

if we plug in infinity in for x.....we get infinity for y (infinity ^ 3 = infinity) ...so A is not correct. Can you check the others following the same guideline? or would you like more help?

Answer 4

More help please, I wasn't there for the lesson on this so I have no idea how to do it. :/ sorry if I seem stupid.

Answer 5

not a problem! and nobody is stupid, you just need to learn it :) so okay...

Answer 6

We can eliminate B) because we know that -infinity ^ 4th power...would turn that negative...positive...so B cannot satisfy that first behavior .

lets check C)...

Answer 7

Okay. for c it would be the same because it would turn it positive.... right?

Answer 8

not quite it's important to remember that you do EXPONENTS before multiplication

-(-infinity^4)

-infinity ^ 4th power does become infinity...however THEN you multiply that by '-' so it DOES become -infinity

Answer 9

Oh. Okay. I did negative times a negative =positive.

Answer 10

Right, and don't worry that's a VERY common mistake. It IS true that a negative times a negative = positive...but remember in THIS case....the negative (-) comes AFTER the exponent...now...on with C)...

Answer 11

Okay.

Answer 12

C) y=-x4+8x2-16

So we HAVE classified that this satisfies the first behavior....but DOES it satisfy the 2nd?

try that...try plugging in infinity for x...and see if you get -infinity

Answer 13

and remember ...exponents BEFORE multiplication....so its

-(infinity^4)

Answer 14

So yes, it does?

Answer 15

it does indeed....so since C) satisfies BOTH behaviors...it must be correct....I just want to see if @dumbcow is correcting something I have done incorrectly lol

Answer 16

Lol. Okay. Thank you for walking me through it. It's a review for my final and it's 80% of my grade.

Answer 17

simple way to remember end behavior