determining symmetry in a graph

點知 about the origin?

if f(x) = f(-x) for all x in the domain of f
then f is symmetric through the origin (also called an even function)

if( f(-x) = -f(x) for all x in the domain of f
then f is symmetric in y-axis (also called an odd function)

至於你講既 symmetric 一個數,
我地就冇學點樣用以上方法check出黎
亦都唔知實際上有冇方法咁樣check

但係如果你對 basic functions 有足夠認識
都會對你好有幫助.. 就好似你既例子 f(x)=|x-2|
佢係一條 linear function, 而佢會將 y < 0 既points反左上去變 y > 0
再想像唔到畫一畫出黎就會明白

1)If a function is symmetrical about the y - axis, then f(x) = f(-x). For example, y = f(x) = x^2. f(-x)= (-x)^2 = x^2 = f(x), so y = x^2 is symmetrical about the y - axis.
2)For f(x) = abs(x), f(-x) = abs(-x) = abs(x) = f(x), so f(x) = abs(x) is symmetrical about the y - axis. Since f(x - a) means f(x) is shifted to the right by a units, f(x) = abs(x-2) means abs(x) is shifted to the right by 2 units, so the line of symmetry is x=2 and f(x) = abs(x-2) is symmetrical about x = 2.
3) For f(x) = 3x + 2, f(-x) is not equal to f(x), so it is not symmetrical about the y-axis.