Question

f(x) =-4x3 + 7x
Determine if its Even,odd, neither

Answer 1

What do u think?

Answer 2

don't we plug -x for x?

Answer 3

yep

Answer 4

yes

Answer 5

so what do u think now

Answer 6

so we get umm

-4(-x)^3+7(-x)
so neither?

Answer 7

it maybe help you to know (-x)^odd =-x^odd
while (-x)^even=x^even

Answer 8

so it will be Odd?

Answer 9

Like what he says even thought i was going to say

Answer 10

yes

Answer 11

How do you know when its neither ?

Answer 12

when you plug in -x
you get neither f(x) or -f(x) back.

Answer 13

huh?

Answer 14

definitions
if f(-x)=f(x) then f is even
if f(-x)=-f(x) then f is odd
so if f(-x) gives you neither f(x) or -f(x) then f is neither odd or even

Answer 15

short cut methods for polynomials:
if all powers are odd, then the function is odd
if all powers are even, then function is even

Answer 16

notice here your -4x^3+7x is polynomial
and the powers are 3 and 1
the powers are both odd
so f is odd
this isn't using definition
it is a short cut way

Answer 17

another example
-4x^3+5
is neither because the powers are 3 and 0
you have a mixture which means it is neither

Answer 18

another example
-4x^2+5
is even because the powers are 2 and 0
both powers are even so the function is even

Answer 19

OHOHOHOHHO you explained it so well :D

Answer 20

that is a short cut method for polynomials though
if the teacher ask you to show work you will need to do the definition

Answer 21

also you do not want to forget the definition because it will be useful for non-polynomials

Answer 22

-3x3 + 9x2 - 3

so this it odd?

Answer 23

I could give you a lot of short cuts for other functions
but it is just too many to list
and so that is why learning the definition is also good

Answer 24

no

Answer 25

you have a mixture so it is neither

Answer 26

you have the powers 3,2, and 0

Answer 27

Wait no neither

Answer 28

@freckles

Answer 29

yes?

Answer 30

so neither?

Answer 31

Ok I guess you didn't read my post above
"you have a mixture so it is neither'

Answer 32

the mixture is pertaining to you have both odd and even powers in the poly

Answer 33

so 5x^2-5
is even

Answer 34

right because you have 2 and 0

Answer 35

ok honestly all you have to say if it wrong or right

Answer 36

Thanks freckles :D

Answer 37

are you talking to me @Tennis5518 ?

Answer 38

I think me copying and pasting what I said above was confirmation enough @Tennis5518

Answer 39

and np @jagr2713

how far do you want to go in math?

Answer 40

CALC!!!!!

Answer 41

just asking because we need to work on using the definition if you do go further

Answer 42

oH, yea some stuff i dont know lol

Answer 43

\[f(x)=\frac{x^2+1}{x^3-x}\]
for example this is not a polynomial
how would you determine if this was even or odd

Answer 44

And yes im talkin about u

Answer 45

umm idk @freckles

Answer 46

ok @Tennis5518 as I said I think copying and pasting what I said above was enough

Answer 47

im gave you a medal cause you deserve it but that to confusing

Answer 48

to the people that doesnt know

Answer 49

anyways....
I don't know what you are talking about...


I'm going to input -x in place of x
\[f(x)=\frac{x^2+1}{x^3-x} \\ f(-x)=\frac{(-x)^2+1}{(-x)^3-(-x)}=\frac{x^2+1}{-x^3+x}=\frac{x^2+1}{-(x^3-x)}=-\frac{x^2+1}{x^3-x}=-f(x)\]

do you see what has happened here ?

Answer 50

like first I input -x
I used what I said earlier (-x)^even=x^even
and (-x)^odd=-x^odd

Answer 51

like (-x)^2=x^2
and (-x)^3=-x^3

Answer 52

now I see that the tops are already the same after doing this
so I played with the bottom to see if it was the same as previous bottom or opposite

Answer 53

Ok whatever you say but im just saying your makeing it complicate it

Answer 54

making*

Answer 55

Oh i get it. Thanks :D

Answer 56

anyways I will stop if you think you are learning too much ? (Doctor Tennis orders :p )

Answer 57

Yea i kinda am haha

Answer 58

k