Determine whether the function is even, odd, or neither. $y = - \sin x \cos x$
A)even
B)odd
C)neither

Question

Quizplus · Accepted Answer

To determine whether a function is even, odd, or neither, we use the following rules:

1. A function is even if f(-x) = f(x) for all x in the domain.
2. A function is odd if f(-x) = -f(x) for all x in the domain.
3. A function is neither even nor odd if it does not satisfy either of the above conditions.

In this case, we have:

f(-x) = -sin(-x)cos(-x) = -(-sin x)(cos x) = sin x cos x

f(x) = -sin x cos x

Since f(-x) = f(x), the function is even.

Determine Whether the Function Is Even, Odd, or Neither y=−sin⁡xcos⁡xy = - \sin x \cos xy=−sinxcosx

Determine Whether the Function Is Even, Odd, or Neither $y = - \sin x \cos x$