F (x) = 3x^4 is even or odd?

Step-by-step explanation:

it's even because f (-x) = f (x)

even function

Step-by-step explanation:

recall that:

a function is EVEN if and only if f (-x) = f (x) for all x in the domain of f

a function is ODD if and only if f (-x) = - f (x) for all x in the domain of f

we observe that for the function

f (x) = 3x^4

because x has been raised to an even power, that f (x) will always be positive (or zero), regardless of whether x is negative or positive.

i. e

f (x) = f (x) and f (-x) = f (x)

This behavior is described by the definition of an EVEN function (given above)

Hence f (x) is an even function