Question

PLEASE HELP GUYSSS?FEMALES What is the end behavior of the function f(x) = x3 + 2x2 + 4x + 5?

Answer 1

IS that 2x2 supposed to be 2 times 2

Answer 2

And is the x3 supposed to be \[x^3\]

Answer 3

yea

Answer 4

there are

f(x)=x^3 +2x^2 +4x +5

Answer 5

^^^^

Answer 6

Okay hold on

Answer 7

So the limit as x approaches infinity?

Answer 8

?

Answer 9

I believe it falls to the left and rises to the right.

Answer 10

and as it approaches negative infinity too, yeah

Answer 11

i just learned this I have no idea what im supopsed to do

Answer 12

Answer choices?

Answer 13

What happens to the values of that function as x approaches -infinity?

Answer 14

@legggoheatnation

Answer 15

Up on the left, up on the right
Up on the left, down on the right
Down on the left, up on the right
Down on the left, down on the right

Answer 16

Down on the left, up on the right

Answer 17

y

Answer 18

Negative numbers cubed on the right decreasing exponentially

Answer 19

idk bout that tbh lol

Answer 20

Did you try using a graphing calculator or plotting points on a drawing?

Answer 21

no

Answer 22

whats tht

Answer 23

A graph...

Answer 24

thanks captain obvious

Answer 25

i mean like what explains it

Answer 26

for negative values of x f(x) will start negative then get closer to 5 when x = 0
so the graph will rise from the left
then continue to rise as x gets more positive

Answer 27

You should say the following:
since the polynomial is a third degree polynomial with a positive leading coefficient then the left side will continue going down and the right side direction will be up forever
also for further information try to type ODD DEGREE POLYNOMIALS

Answer 28

- a very rough drawing lol

Answer 29

Hope that helps :)

Answer 30

hmm iTHInk i get it thanks man

Answer 31

HI!!

Answer 32

this is much easier than it looks

Answer 33

the degree is odd, and the leading coefficient is 1
the end behavior is the same for any polynomial of odd degree and positive leading coefficient, i.e .the end behavior is the same as \(y=x\)

Answer 34

what would the answer be then?

Answer 35

misty's answer is the best one

Answer 36

\[f \prime \left( x \right)=3x^2+4x+4=3\left( x^2+\frac{ 4 }{ 3 }x \right)+4\]
\[=3\left( x^2+\frac{ 4 }{ 3 }x+\frac{ 4 }{ 9 }-\frac{ 4 }{ 9 } \right)+4\]
\[=3\left( x+\frac{ 2 }{ 3 } \right)^2-\frac{ 4 }{ 3 }+4\]
\[=3\left( x+\frac{ 2 }{ 3 } \right)^2+\frac{ 8 }{ 3 }>\frac{ 8 }{ 3 }>0\]
f(x) is always increasing.