Is f(x) = xsin(x) even, odd or neither?
f(a) = asin(a)
f(−a) = −asin(−a)
but, since y = sinx is odd,
= −a(−sin(a)) = asin(a)
So f(a) = f(−a)
therefore, y = xsinx is even.
Use the eTool below to examine the graph.
Click the link at right for the full version of the eTool: Calc 4-22 HW eTool