Question

PLEASE HELP
Give an example of a function that is neither even nor odd and explain algebraically why it is neither even nor odd.

This is a writing portion and I always get it wrong

Answer 1

@welshfella

Answer 2

do you have to make a example on your own or?

Answer 3

yes, but I have no idea what or how to make my eample

Answer 4

example*

Answer 5

@zepdrix

Answer 6

ok well you want a function to have both, or neither of those properties so ive had this question before in another room here is 1 i got u can use it you want it to have these even function f(x) = f(-x) odd function f(x) = -f(x) ok soo

x^3 + x^2

Answer 7

hope it helped!

Answer 8

if u need anymore help i have my own room to help ppl the KG1975 Help Room!

Answer 9

Hi kg1975
you have an error or a typo there
for an odd function -f(x) = f(-x)

Answer 10

What should I put for my answer?

Answer 11

I'd write a complex cubic function - chances are that its neither odd or even
2x^3 - 3x^2 -6x + 4

Answer 12

Then see if f(x) = f(-x) or -f(x) = f(-x)

i expect they wont be true

Answer 13

Use a function with some terms having x raised to an even power and some terms having x raised to an odd power and a constant term.

Answer 14

Yes - which is like the one i've written.

Answer 15

I also have to explain it, how would I do that?

Answer 16

f(x) = 2x^3 - 3x^2 -6x + 4
f(-x) = 2(-x)^3 - 3(-x)^2 - 6(-x) + 4 = -2x^3 - 3x^2 + 6x + 4
So f(x) is not = f(-x) so the function is not even

now find -f(x) and show that its not = f(-x) and you've finished the proof.

Answer 17

I don't know how to do that, could you help me step by step? :(

Answer 18

@zepdrix

Answer 19

@kellyspeakslouder
As mentioned before,
even functions satisfy f(x)=f(-x), and
odd functions satisfy f(x)=-f(-x).
However, ANY function which is a sum of an odd function an even function cannot satisfy either condition, therefore it will be neither odd nor even.
Examples of odd functions: 1/x, x, x^3, x^5, sin(x), tan(x), or any sum of the preceding.
Examples of even functions: K, x^2, x^4, x^6, ... cos(x) or any sum of the preceding.
Examples of neither odd nor even: sum of an odd and an even function, e^x, log^x, etc.

Answer 20

thanks but I still don't know what to write down.. :(

Answer 21

@zepdrix

Answer 22

When you get a function with exponents all "even", it's an even function, when you have a function with exponents all "odd" it means it's an odd function, but when you have a function with both "even" and "odd" exponents. The function is neither, meaning if you plug in a "negative value" into the function, the function will partially change but not entirely. So it'd be a neither function.
odd function: f(x)=7x^5 + 3x^3+ x^1
even function: f(x)=2x^4++3x^2+5
neither function: f(x)=-3x^4-2x^1-5

Answer 23

is this good? @zepdrix

Answer 24

It looks good. But bear in mind that odd and even functions are not limited to polynomials. Reviewing the examples I gave for odd, even and neither might help.