函數(2)
Author: 藍邦偉  老師

$ O $

$ 幾個常見的函數(2) $

1

2

$ 定義域 $

$ 值域 $

$ R=\left\lbrace  y∈\mathbb{R}|y≥0\right\rbrace  $

$ R=\left\lbrace  y∈\mathbb{R}|y≤0 \right\rbrace  $

$ D=\left\lbrace x∈\mathbb{R}|x≠0  \right\rbrace  $

$ R=\left\lbrace  y∈\mathbb{R}|y≠0\right\rbrace  $

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: 0.73 * Corner[1] + 0.27 * 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])
r = 1 (slider from 1 to 4, step 1)
n = 0 (slider from 0 to 5, step 1)
text2: "$ f_2(x)=-\sqrt{" + (LaTeX[r^(2)]) + "-x²} $"
text1: "$ f_1(x)=\sqrt{" + (LaTeX[r^(2)]) + "-x²}$"
f_2(x) = -sqrt(r^(2) - x^(2))
f_1(x) = sqrt(r^(2) - x^(2))
h = 0 (slider from -5 to 5, step 0.1)
a = 1 (slider from 1 to 5, step 1)
f_3(x) = a * sqrt(x - h)
f_4(x) = -a * sqrt(x - h)
text4: "$ f_4(x)=-" + (LaTeX[If[a ≠ 1, abs(a), ""]]) + "\sqrt{x" + (LaTeX[If[h > 0, "-", If[h ≠ 0, "+", ""]]]) + "" + (LaTeX[If[h ≠ 0, abs(h), ""]]) + "} $"
text3: "$ f_3(x)=" + (LaTeX[If[a ≠ 1, a, ""]]) + "\sqrt{x" + (LaTeX[If[h > 0, "-", If[h < 0, "+", ""]]]) + "" + (LaTeX[If[h ≠ 0, abs(h), ""]]) + "} $"
k = 1 (slider from 1 to 5, step 1)
text5: "$ f_5(x)=\frac{1}{x^{" + (LaTeX[If[k ≥ 2, k, ""]]) + "}} $"
f_5(x) = 1 / x^(k)
A = (-10.127805768529127, 2.6581961436787807)
b = false
c = false
D_1: "$ D=\left\lbrace x∈\mathbb{R}|-" + (LaTeX[r]) + "≤x≤" + (LaTeX[r]) + " \right\rbrace  $"
R_1: "$ R=\left\lbrace y∈\mathbb{R}|0≤y≤" + (LaTeX[r]) + " \right\rbrace  $"
D_2: "$ D=\left\lbrace x∈\mathbb{R}|-" + (LaTeX[r]) + "≤y≤" + (LaTeX[r]) + " \right\rbrace  $"
D_3: "$ D=\left\lbrace x∈\mathbb{R}|x≥" + (LaTeX[h]) + " \right\rbrace  $"
D_4: "$ D=\left\lbrace x∈\mathbb{R}|x≥" + (LaTeX[h]) + " \right\rbrace  $"
R_6: "$ R=\left\lbrace y∈\mathbb{R}|-" + (LaTeX[r]) + "≤y≤0 \right\rbrace  $"