Algebra function problem. Help!?

Question

how do i tell if this is a odd or even function?

F(x) = 3x^4 - 5

thanks,
FE

I want to know how to tell if its even or not, i dont just want the answer

Answer 1

even

If f(-x) = f(x) then f(x) is even.
But, if f(-x) = -f(x) then f(x) is odd function.

Here, f(-x) = 3(-x)^4 - 5 = 3x^4 - 5 = f(x).
So f(x) is even function.

Answer 2

An even function has the property that f(-x)=f(x)

so F(-x) = 3(-x)^4 - 5 = 3x^4 - 5 = F(x) so it is indeed even.

Similarly, a function that satisfies f(-x)=-f(x) is considered odd.

The "evenness" and "oddness" of a function can come in very handy when dealing with complex problems.

Answer 3

To check the given function is even or odd put -x for x
If f(-x) = f(x) then the given function is EVEN otherwise its odd [f(-x) = - f(x)]
F(-x) = 3(-x)^4 - 5 = 3x^4 - 5 = F(x)
Hence the given function is even function.

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Answer 4

Easy way to determine for polynomial functions:

All exponents even represents an EVEN function

All exponents odd represents an ODD function

Remember....constants are c* X^0...that is constants are considered to have even exponents as c is a coefficient of x^0

Answer 5

A function is even if f(x) = f(-x).

A function is odd if -f(x) = f(-x).

Just plug in x=1 and x=-1 and compare the results.