Question

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term.
-3x5 + 9x4 + 5x3 + 3

Answer 1

@Lakeekee_

Answer 2

nomallyi would factor the polynomial orr factor by grouping the polynomial but you cant factor this one so im not sure on the answer im sorry

Answer 3

@iGreen @KamiBug @amberxoxo @phi

Answer 4

thnx for trying doe @Lakeekee_

Answer 5

yw boo @Tazmaniadevil and @LichKing

Answer 6

@cupcakerain

Answer 7

All even degree polynomials
\[x^2, x^4, x^6, \ldots\]
are such that as you tend towards negative or positive infinity (i.e. as you go all the way to the left or all the way to the right), both ends either go up or down. Just think about the graph of a parabola x^2.
All odd degree polynomials
\[x^3, x^5, x^7, \ldots\]
are such that one end goes up and the other goes down. For the graph of x^3, as you go to the left, you tend towards more negative y values (the graph goes down) and as you go to the right, you tend towards more positive y values (the graph goes up).
The leading degree of your polynomial is 5 (odd), so that suggests that one end goes up and the other goes down. However, the leading coefficient is negative, suggesting that it is flipped over the x-axis. What do you think the behavior is like?
If you're confused, you can always plot the polynomial.

Answer 8

ya this dude just kilt me brain no im even more confused sombody got the how to do this problem for dummies explanation plz lol

Answer 9

@wyattp17 @VortexAlliby

Answer 10

hhaha gimme a sec

Answer 11

nvm... no ducking idea sorry tazz

Answer 12

zammmitttt

Answer 13

@Directrix

Answer 14

Here's a plot of x^2 and x^3 to help you see

Answer 15

Notice how for x^2, both ends go up while for x^3, one end goes up while the other goes down.

Answer 16

@Directrix plz come and help i need to got to work and this people are confusing me i need your guidance oh great master

Answer 17

http://msenux.redwoods.edu/IntAlgText/chapter6/section1.pdf go to this website boo it will explain how to do it

Answer 18

@igreen help me master of math

Answer 19

ur getting ignored *taunts you* ur getting ignored ha hah ha ha ha ha *chants*

Answer 20

jkjk

Answer 21

https://www.desmos.com/calculator/rsotev49ri

Answer 22

There's a graph of it..

Answer 23

@Lakeekee_ your goin to let her tuant you boo like that shame jk jk jk lol

Answer 24

ok so how do i do this problem

Answer 25

Have you looked at the graph that @iGreen posted?

Answer 26

yes i did but it says to What is the end behavior of the graph? Describe the end behavior and provide the leading term. so how do i do this

Answer 27

I believe this graph is negative..therefore the leading term would be negative..

Answer 28

leading coefficient*

Answer 29

O_O ok i guess that makes since lol

Answer 30

The leading term has the highest power of x:

So what is it?

P{x) = -3x5 + 9x4 + 5x3 + 3

Answer 31

um im guessing x5

Answer 32

i ment 5 x lol

Answer 33

Five is correct.

Answer 34

So, this is the leading term: -3x5

Answer 35

ook

Answer 36

In the end, it does not matter what these terms do: + 9x4 + 5x3 + 3

Answer 37

They are along for the ride.

Answer 38

-3x^5 is the driver.

Answer 39

The question is about the end behavior of this: P(x) = -3x5 + 9x4 + 5x3 + 3

Answer 40

I find this very helpful:

http://hotmath.com/hotmath_help/topics/end-behavior-of-a-function.html

Answer 41

That is the same as asking how -3x^5 behaves as x gets larger and larger (as x approaches infinity)

Answer 42

ok i understand that

Answer 43

Is 5 an odd or even number? @Tazmaniadevil

Answer 44

odd

Answer 45

Look at the lead term again: -3x^5

Negative 3 times x raised to the 5th power

Answer 46

ok so what am i looking for

Answer 47

x raised to the 5th power

Answer 48

Right, so it's Degree is Odd, and I said it's Leading Coefficient is negative..so looking at the link I sent you, look at the table and see which one is both 'Odd' and 'Negative', then look at the End Behavior..it will give you your answer.

Answer 49

Go ahead and finish @iGreen

Answer 50

@cupcakerain @Lakeekee_ has something to tell you lol

Answer 51

sure :) go ahead girl

Answer 52

ok thianks guys i think i got the rest

Answer 53

Okay, what did you come up with the End Behavior?

Answer 54

dont sas my maan jkjkjkjk lol

Answer 55

thas all u wanna say to me?

Answer 56

cat fight do it do it do it

Answer 57

i mena dont be fighting in my math question fyall dont wanna get in troulbe now ya here

Answer 58

sorry i got graph is negative..therefore the leading coefficient would be negative.. becuase it has a negative ending int he eqaution

Answer 59

am i right @iGreen

Answer 60

Yes..

The link I gave you says that if the Leading Coefficient is Negative, and the Degree is Odd, the end behavior will be as P(x) approaches positive infinity, x will approach negative infinity. And as x approaches positive infinity, P(x) will approach negative infinity.

Answer 61

thnx again @iGreen you da best

Answer 62

No problem.

Answer 63

And GO BRONCOS! ;P

Answer 64

^^yesh^^

Answer 65

^ ALWAYS AND FOREVRE BRONCOS RULE THE NFL YEEEE BOIIIII!!!!!!

Answer 66

AND THOSE THAT APEAL WHAT I SAY SHAL HAVE A LONG DEFEING FEATH

Answer 67

i menat death lol