Determine whether the function f(x) = 3x4 is even
or odd.

even

Step-by-step explanation:

f(-x)=f(x) implies the function is even.

f(-x)=-f(x) implies the function is odd.

There are some things you should know before we being this problem:

Examples:

Let's begin the problem:

Must plug in -x.  Both definitions require this part.

I replace

So since we have f(-x)=f(x), the conclusion is that f is even.

to test a function's behaviour if it's even or odd, we simply use -x, namely check what f(-x) give us, if the result is the same as the original f(x), then it's even, if the result is a negative original, namely -f(x), then is odd.