is symmetric about x=1/2, but not x=1.
try to translate 1/2 unit left
Hi all ----
I actually get part (ii) of this question - but I'm just curious - how can I formally prove the symmetry? The question doesn't ask this but I'm just curious. The green box is the solution.
Part (ii) --- I can see that reaches maximum when .
But it also looks like is symmetric about . How would I prove this?
I know how to do this for ---
is symmetric about because so .
Thanks a lot ---
do you know how to translate the graph of a function horizontally? If the question want you to prove f(x) is symmetry about x=c, then you need to translate the graph c unit left/right.
For example, you want to prove function (x-1)^4 is symmetry about x=1. you need to translate the function 1 unit left, the function will become (x-1+1)^4 = x^4. Obviously it's symmetry about x=0, i.e. x=0 is its symmetry axis of x^4. If you translate x^4 back to (x-1)^4, the whole graph will move 1 unit right, i.e. the symmetry axis will move 1 unit right too. Therefore, (x-1)^4 is symmetry about x=1.
If a figure is translated either horizontally or vertically, only its position changed, its shape, size, pointing direction DOESN'T change. So I think you know how to do it know.