指數函數的對稱

f(x)=2^x

g(x)=\left(  \frac{1}{2} \right)^x 

如圖所示，\;兩圖形
對稱於\;y\;軸

證明：

設A(-α,β)在\;g(x)=\left( \frac{1}{2}  \right)^x上 

⇒β=\left( \frac{1}{2}  \right) ^{-α}=2^α

故B(α,β)在f(x)=2^x上

A(-α,β)

f(x)=2^x

g(x)=\left( \frac{1}{2}  \right) ^x

B(α,β)

Forward

f_1(x) = 2^(x)
s = 0 (slider from 0 to 7, step 1)
A = Point(Segment[(x(Corner[1]), 0), (log(2, y(Corner[4])), 0)])
f_0(x) = x^(2)
A' = Mirror(A, x = 0)
f_2(x) = 2^((-x))
u_1 = Vector(A, (x(A), f_1(x(A))))
u_2 = Vector((x(A'), f_2(x(A'))), A')
a_0 = Vector((x(A), f_1(x(A))), (x(A'), f_2(x(A'))))
B = Point(f_2)
B' = Mirror(B, yAxis)