函數的伸縮平移與對稱
Author: 藍邦偉  老師

$ O $

$ f(x)= $

1

$ 函數圖形的伸縮平移與對稱 $

1

$ 顯示平移變量 $

k = 0 (slider from -5 to 5, step 0.1)
f(x) = x^(2) - sin(x) + lg(x) - 2^(x)
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
Q_2: 0.7 * Corner[1] + 0.3 * Corner[2]
O = (0, 0)
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])
a = 1 (slider from x(Q_2) to x(Corner[2]), step 0.01)
b = 2 (slider from 1 to 10, step 1)
inputBox1 = Textfield(f)
f_3(x) = -f(-x) + k
f_4(x) = f(a - x) + k
f_5(x) = 1 / b * f(x) + k
f_6(x) = b * f(x) + k
f_2(x) = -f(x) + k
n = 0 (slider from 0 to 8, step 1)
text1: "$ y=f(-x)" + (LaTeX[If[k > 0, "+", If[k < 0, "-", ""]]]) + "" + (LaTeX[If[k ≠ 0, abs(k), ""]]) + " $"
f_1(x) = f(-x) + k
text2: "$ y=-f(x)" + (LaTeX[If[k > 0, "+", If[k < 0, "-", ""]]]) + "" + (LaTeX[If[k ≠ 0, abs(k), ""]]) + " $"
text3: "$ y=-f(-x) " + (LaTeX[If[k > 0, "+", If[k < 0, "-", ""]]]) + "" + (LaTeX[If[k ≠ 0, abs(k), ""]]) + "$"
c = false
text4: "$ y=f(a-x) " + (LaTeX[If[k > 0, "+", If[k < 0, "-", ""]]]) + "" + (LaTeX[If[k ≠ 0, abs(k), ""]]) + "$"
text5: "$ y=\frac{1}{b}\cdot f(x)" + (LaTeX[If[k > 0, "+", If[k < 0, "-", ""]]]) + " " + (LaTeX[If[k ≠ 0, abs(k), ""]]) + "$"
L_4: x = a / 2
text_{41}: "$ x=\frac{" + (LaTeX[a]) + "}{2} =" + (LaTeX[a / 2]) + "$"
A = (-9.707647754071886, 2.8491770593411587)
text6: "$ y=b\cdot f(x) " + (LaTeX[If[k > 0, "+", If[k < 0, "-", ""]]]) + "" + (LaTeX[If[k ≠ 0, abs(k), ""]]) + "$"
f_7(x) = f(b * x) + k
text7: "$ y=f(bx)" + (LaTeX[If[k > 0, "+", If[k < 0, "-", ""]]]) + "" + (LaTeX[If[k ≠ 0, abs(k), ""]]) + " $"
text8: "$ y=f(\frac{x}{b}) " + (LaTeX[If[k > 0, "+", If[k < 0, "-", ""]]]) + "" + (LaTeX[If[k ≠ 0, abs(k), ""]]) + "$"
f_8(x) = f(x / b) + k
B = (-4.608457305886261, 4.472514842471413)
Fcn: "$ y=" + (LaTeX[If[n ≟ 1, f_1, If[n ≟ 2, f_2, If[n ≟ 3, f_3, If[n ≟ 4, f_4, If[n ≟ 5, f_5, If[n ≟ 6, f_6, If[n ≟ 7, f_7, f_8]]]]]]]]) + " $"
text9: "$ f(x)=" + (LaTeX[f]) + " $"
C = (0.7581064242267, 5.0645556810248)