Even or odd functions

f(x) = { x+π, x∈[-π, 0]
{ -x+π, x∈(0, π)

This is a piecewise function, and i'm aware that it is a even function, however I do not know why it is,

I tried say x = π/2, hence

f(x=π/2) = 3π/2, x∈[-π, 0]
π/2, x∈(0, π)

f(-x=-π/2) = π/2, x∈[-π, 0]
3π/2, x∈(0, π)

Here does f(x) = f(-x), i don't see how it does since the range which each value lie in is different. But i am informed that it is an even function.

Any help would be gratefull. Thank you.

Try graphing the functions.

Once this is graphed, an even function will be symmetric about the y-axis.