Determine if the function is even, odd, or neither.
-$$f ( x ) = - 3 x ^ { 4 } + 2 x - 8$$
A) Even
B) Odd
C) Neither

Question

Quizplus · Accepted Answer

To determine if a function is even or odd, we look at how the function behaves when we substitute –x for x.

If we substitute –x for x in an even function, we get the same function back. In other words, if f(x) = f(–x), then the function is even.

If we substitute –x for x in an odd function, we get the opposite of the original function. In other words, if f(–x) = –f(x), then the function is odd.

If neither of these conditions holds, then the function is neither even nor odd.

Let's test this function for evenness or oddness:

$$f ( - x ) = - 3 ( - x ) ^ { 4 } + 2 ( - x ) - 8 = - 3 x ^ { 4 } - 2 x - 8 $$

Since f(-x) is not equal to f(x) and it is not equal to -f(x), the function is neither even nor odd.

Determine If the Function Is Even, Odd, or Neither f(x)=−3x4+2x−8f ( x ) = - 3 x ^ { 4 } + 2 x - 8f(x)=−3x4+2x−8

Determine If the Function Is Even, Odd, or Neither $f ( x ) = - 3 x ^ { 4 } + 2 x - 8$