what are the ways to remember how the end behavior will be for graphing a polynomial function, like if the leading coefficient is positive and the degree is even what does it look like? leading coefficient +, and degree odd? leading -, degree even? leading -, odd?

- anonymous

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- amistre64

i know...i know...pick me!!

- anonymous

hahah thanks

- amistre64

all even degreed function with a positive first term will have ends that go up in both directions like a "U".
if the first term is negative, it flips it over and the ends will go down like a turned over bowl...

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## More answers

- amistre64

all odd degreed function behave like a slanted line. if the first term is positive, they go uphill.... left side down, right side up

- amistre64

if its negative it flows down hill; left side up, right side down.... make sense?

- anonymous

you just saved my life. thank you <3

- amistre64

No prob :)

- anonymous

so if its still and even degreed function but just with a negative first term it is like a frown?

- amistre64

Yes, exactly....kinda depressing....

- anonymous

haha

- anonymous

can i give an example?

- anonymous

....

- amistre64

sorry, left for a sec.... yeah, ive me an example ...

- amistre64

*give....

- anonymous

alright.

- anonymous

\[x ^{4}+2x ^{3}-16x ^{2}-2x+15\]

- anonymous

positive lead, even degree, smiley face?

- amistre64

thats correct; all the other stuff does is make it dance around, but when the value of "x" gets HUGE, all that matters is the "x^4"..

- amistre64

HUGE being relative, -infinity or infinity, both tend to be pretty massive :)

- amistre64

How about this one:
-4x^7 + 6x^2 -9; whats it doin at the ends?

- anonymous

hahah gets huge. good one.

- amistre64

remember "negative" is down....downhilll.....

- anonymous

ok ummm left up, right down

- amistre64

very good :) youre a natural

- anonymous

i get huge. i mean big. i mean good.

- anonymous

im a girl, just saying,

- amistre64

:) my daughters a girl too

- amistre64

how about:
9834x^743858 + 14x^32 -90 ?

- anonymous

nice.
postive, even. smiley

- anonymous

positive*

- amistre64

nuthin to it right? :)

- anonymous

ehh.

- amistre64

is that your impersonation of a canadian...

- amistre64

have you studied rational functions yet? with their vertical and horizontal asymptotes?

- anonymous

no not yet

- amistre64

we'll save that for another day then :) Ciao...

- anonymous

thank you!

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