函數圖形的鉛直線檢驗法
Author: 藍邦偉  老師

$ O $

$ 函數圖形的鉛直線檢定法 $
$\;$
$座標平面上，\;函數圖形與$
$任一鉛直線至多交於一點.$

$ x^2+y^2=r^2 $

$ y^2=4cx $

$ x^2=4cy $

$ y=\left\vert |x|-c|\right\vert  $

$ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 $

$ y=mx+k $

$ y=\sqrt{r^2-x^2} $

$ y=-\sqrt{r^2-x^2} $

$ y=2\sqrt{cx} $

$ y=-2\sqrt{cx} $

$ y=k $

$ y=b\cdot \sqrt{\frac{x^2}{a^2}-1} $

$ \frac{x^2}{a^2} +\frac{y^2}{b^2}=1$

1

$ 顯示圖形方程式 $

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.75 * Corner[1] + 0.25 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
n = 0 (slider from 0 to 15, step 1)
f_7(x) = sqrt(4 - x^(2))
f_8(x) = -sqrt(4 - x^(2))
f_4(x) = abs(abs(x) - 1)
f_9(x) = 2 * sqrt(x)
f_{10}(x) = -2 * sqrt(x)
f_{12}(x) = 2 * sqrt(x^(2) - 1)
P_1 = (-2.182999676973997, 4.1096511027128875)
P_2 = (1.6175205447074232, 2.5436075942813483)
P_3 = (-1.8583321203479461, 1.1685450015121919)
t = -2.201363219137251 (slider from x(Q_2) to x(Corner[2]), step 0.0010)
P_4 = Point(u)
L_{13} = PolyLine(P_1, P_2, P_3, P_4)
f_{15}(x) = 5 * ℯ^((-x^(2)) / 2) / (sqrt(2 * π) * abs(1))
f_{16} = Mirror(f_{15}, a)
L: x = t
A_1, B_1 = Intersect(c_1, L)
A_2, B_2 = Intersect(Γ_2, L)
A_4 = Intersect(f_4, L, (-2.201363219137251, 1.2013632191372512))
A_5, B_5 = Intersect(Γ_5, L)
A_6 = Intersect(L, L_6)
A_7 = Intersect(f_7, L, (-0.9583632191372509, 1.7554315538365162))
A_8 = Intersect(f_8, L, (-0.9583632191372509, -1.7554315538365162))
A_9 = Intersect(f_9, L, (3.684636780862748, 3.8390815468613053))
A_{10} = Intersect(f_{10}, L, (3.684636780862748, -3.8390815468613053))
A_{11} = Intersect(L_{11}, L)
A_{12} = Intersect(f_{12}, L, (-2.201363219137251, 3.9222442670340265))
A_{13}, B_{13}, C_{13} = Intersect(L, L_{13})
A_{14}, B_{14} = Intersect(Γ_{14}, L)
A_{15} = Intersect(f_{15}, L, (-2.201363219137251, 0.1768416407235363))
B_{16} = Mirror(A_{15}, a)
A_{16} = Mirror(B_{16}, xAxis)
A_3 = Intersect(Γ_3, L)
A = (-9.745843937204361, 0.4428175219951371)
b = false