Transformation of Graph

法1:
y=f(x)左移3單位得 y=f(x+3)
y=f(x+3)=F(x),左右縮小為1/2倍,得 y=F(2x)=f(2x+3)
y=f(2x+3)=G(x),對稱於y軸得 y=G(-x)=f(-2x+3)

法2:
y=f(x)左右對稱於y軸得y=f(-x)
y=f(-x)=F(x),左右縮為 1/2 倍,得y=F(2x)=f(-2x)
y=f(-2x)=G(x),右移 3/2得y=G(x- 3/2)= f[-2(x-3/2)]=f(-2x+3)

如果要將 f(x) 移到 f(-ax+b), 有幾個方法

Method 1:
shift b units to right, f(x+b) , and let f(x+b) = g(x)
then compress a units, g(ax) = f( (ax) + b ) = f(ax+b), and let f(ax+b) = h(x)
then reflect along y-axis, h(-x) = f( a(-x) + b ) = f(-ax+b)

還有method 2, method 3, method 4.... 讀者可自己嘗試.