Question

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?

Answer 1

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

Answer 2

hahah thanks

Answer 3

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...

Answer 4

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

Answer 5

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

Answer 6

you just saved my life. thank you <3

Answer 7

No prob :)

Answer 8

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

Answer 9

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

Answer 10

haha

Answer 11

can i give an example?

Answer 12

....

Answer 13

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

Answer 14

*give....

Answer 15

alright.

Answer 16

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

Answer 17

positive lead, even degree, smiley face?

Answer 18

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"..

Answer 19

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

Answer 20

How about this one:

-4x^7 + 6x^2 -9; whats it doin at the ends?

Answer 21

hahah gets huge. good one.

Answer 22

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

Answer 23

ok ummm left up, right down

Answer 24

very good :) youre a natural

Answer 25

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

Answer 26

im a girl, just saying,

Answer 27

:) my daughters a girl too

Answer 28

how about:

9834x^743858 + 14x^32 -90 ?

Answer 29

nice.

postive, even. smiley

Answer 30

positive*

Answer 31

nuthin to it right? :)

Answer 32

ehh.

Answer 33

is that your impersonation of a canadian...

Answer 34

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

Answer 35

no not yet

Answer 36

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

Answer 37

thank you!