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Mathematics 19 Online
OpenStudy (anonymous):

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?

OpenStudy (amistre64):

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

OpenStudy (anonymous):

hahah thanks

OpenStudy (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...

OpenStudy (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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

you just saved my life. thank you <3

OpenStudy (amistre64):

No prob :)

OpenStudy (anonymous):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

haha

OpenStudy (anonymous):

can i give an example?

OpenStudy (anonymous):

....

OpenStudy (amistre64):

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

OpenStudy (amistre64):

*give....

OpenStudy (anonymous):

alright.

OpenStudy (anonymous):

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

OpenStudy (anonymous):

positive lead, even degree, smiley face?

OpenStudy (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"..

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

hahah gets huge. good one.

OpenStudy (amistre64):

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

OpenStudy (anonymous):

ok ummm left up, right down

OpenStudy (amistre64):

very good :) youre a natural

OpenStudy (anonymous):

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

OpenStudy (anonymous):

im a girl, just saying,

OpenStudy (amistre64):

:) my daughters a girl too

OpenStudy (amistre64):

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

OpenStudy (anonymous):

nice. postive, even. smiley

OpenStudy (anonymous):

positive*

OpenStudy (amistre64):

nuthin to it right? :)

OpenStudy (anonymous):

ehh.

OpenStudy (amistre64):

is that your impersonation of a canadian...

OpenStudy (amistre64):

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

OpenStudy (anonymous):

no not yet

OpenStudy (amistre64):

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

OpenStudy (anonymous):

thank you!

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