Question

How do you determine if `x sin x` is an even or odd function?

Answer 1

even function

Explanation:

To determine wether a function is odd/even apply the following.

• If f(x) = f( -x) , then f(x) is even

Even functions are symmetrical about the y-axis.

• If f( -x) = - f(x) , then f(x) is odd

Odd functions have symmetry about the origin.

Test for even

f( -x) = (-x)sin(-x) and sin(-x) = - sinx

`rArr f(-x) = -x.( -sinx )= xsinx = f(x)`

thus xsinx is an even function.

This is graph of xsinx. Note symmetry about y-axis.
graph{xsinx [-10, 10, -5, 5]}