Which statement best describes how to determine whether f(x) = x4 – x3 is an even function?
Function is even if it satisfies following relation:
Or, in words: Function is odd if the substitution of x with −x results in output opposite to f(x).
Graphically, function is odd if its graph is symmetric with respect to origin.
Now, to check if given function is odd, we substitute x with −x:
Function would be odd if we obtained −f(x) =−(x4−x3) = −x4+x3.
Since this was not our result of substitution, function is not odd.