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?
i know...i know...pick me!!
hahah thanks
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...
all odd degreed function behave like a slanted line. if the first term is positive, they go uphill.... left side down, right side up
if its negative it flows down hill; left side up, right side down.... make sense?
you just saved my life. thank you <3
No prob :)
so if its still and even degreed function but just with a negative first term it is like a frown?
Yes, exactly....kinda depressing....
haha
can i give an example?
....
sorry, left for a sec.... yeah, ive me an example ...
*give....
alright.
\[x ^{4}+2x ^{3}-16x ^{2}-2x+15\]
positive lead, even degree, smiley face?
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"..
HUGE being relative, -infinity or infinity, both tend to be pretty massive :)
How about this one: -4x^7 + 6x^2 -9; whats it doin at the ends?
hahah gets huge. good one.
remember "negative" is down....downhilll.....
ok ummm left up, right down
very good :) youre a natural
i get huge. i mean big. i mean good.
im a girl, just saying,
:) my daughters a girl too
how about: 9834x^743858 + 14x^32 -90 ?
nice. postive, even. smiley
positive*
nuthin to it right? :)
ehh.
is that your impersonation of a canadian...
have you studied rational functions yet? with their vertical and horizontal asymptotes?
no not yet
we'll save that for another day then :) Ciao...
thank you!
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