众所周知,函数奇偶性、周期性及图象的对称性在函数中占有极其重要的地位,历来为命题者所钟爱,那么这些性质到底有哪些联系呢?本文先从一道高考题谈起.题目(05年广东高考第19题)设函数f(x)在R上满足f(2-x)=f(2+x),f(7-x)=f(7+x),且在闭区间[0,7]上,只有f(1)=f(3)=0.(Ⅰ)试判断 As we all know, function parity, periodicity and image symmetry occupy an extremely important position in the function, which has always been favored by proponents. So what are these properties in the end? In the Guangdong college entrance examination in 2005 question 19) Let f (2-x) = f (2 + x) and f (7-x) = f (7 + x) satisfy the function f [0,7], only f (1) = f (3) = 0. (I) try to judge