SOLUTION: determine whether f(x)=-sin x is even, odd, or neither.

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Question 468453: determine whether f(x)=-sin x is even, odd, or neither.
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Odd function:
-f%28x%29+=+f%28-x%29
Even function:
f%28x%29+=+f%28-x%29
f%28x%29+=+-sin%28x%29
-f%28x%29+=+sin%28x%29
The graph is reflected about the x-axis, and is not the same as -sin%28x%29.
f%28-x%29+=+sin%28-x%29
The graph is reflected about the y-axis, and is the same as -sin%28x%29.
The graph is an even+function.


+graph%28+500%2C+500%2C+-20%2C+20%2C+-10%2C+10%2C+-sin+%28x%29%29+


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
determine whether f(x)=-sin x is even, odd, or neither.
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f(x)=-sin x
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f(-x) = -sin(-x) = -[-sin(x)] = sin(x)
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-f(-x) = -sin(x)
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Since f(x) = -f(-x), f is odd
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Cheers,
stan H.