I know what it means by by even, or odd, function. i also know what it means graphically. My question is how to find a whether a function is even, or odd? if the function is defined in three intervals or more than three intervals. Consider a function F(x) defined in the interval (a,d) F(x)= [ p(x) where x belong to the interval (a, b); q(x) where x belong to the interval (b, c); r(x) where x belong to the interval (c, d); ] The particular problem I'm faced with is: F(x)= [ p(x)=0 where x belong to the interval (-8,0); q(x)=4 where x belong to the interval (0,4); r(x)=8 where x belong to the interval (4,8); ]
You say you "know what it means by even, or odd, function" so just apply that. In particular F(-5)= 0. F(5)= 8. That tells you all you need to know.