Determine whether the function f(x) = 3x^4 is even or odd

To determine whether the function f(x) = 3x^4 is even or odd, we can use the definitions of even and odd functions.

A function is considered even if, for every x in the domain of the function, f(-x) = f(x). Conversely, a function is odd if f(-x) = -f(x).

Let’s apply these definitions to our function:

f(-x) = 3(-x)^4
      = 3(x^4)  
      = 3x^4
      = f(x)

Since we find that f(-x) = f(x), we can conclude that the function f(x) = 3x^4 is an even function.

In summary, the function f(x) = 3x^4 is even because it satisfies the condition f(-x) = f(x) for all x in its domain.