Question

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

Answer 1

even function f(x) = f(-x)
odd function f(x) = -f(x)

Answer 2

you want a function to have both, or neither of those properties

Answer 3

x^3 + x^2, for instance

Answer 4

why? because x^2 is even and x^3 is odd

therefore for any value of x, you will have both even and odd answers

which is neither even or odd

Answer 5

in fact, any function of the form x^n + x^(n-1) will work

assuming n is positive

Answer 6

Even functions fall into the category:
\[f(x) = f(-x)\]
if you replace all of the x's with negative x's it should be the same algebraically. Which means that the function is the same (symetrical) about the y axis.

Odd Functions, however, are the negative magnitude when a negative value is place in for x
\[f(-x) = -f(x)\]
if you replace all the x's of f(x) you'll get the same magnitude but with a negative sign. these functins are symetrical around the line \[y = x\]

To create a function that is neither odd nor even you must ensure that at least one term in the function violates each of those two rules above. for instance to ensure that it is not even you should include an x term to a odd degree ie:
\[f(x) = x ^{2n-1}\]
, and to avoid being odd you must include an x term to an even degree, ie.
\[f(x) = x ^{2n}\]