m

x_P

y_P

x_Q

y_Q

Hilfe einblenden

gl1: x = 1
P = (1, 1)
x0: x(P)
A: (4 | 3)
B: (6 | 3)
Vieleck1, gDreieck, hDreieck, iDreieck, C = Polygon(A, B, 3)
d: 0.5
PunkteQ = Sequence(Sequence[(i | j), j, -10, 10, d], i, x0 + d, 10, d)
Q = (2, 3)
R: (x(Q) | y(P))
m: (y(Q) - y(P)) / (x(Q) - x(P))
y0: y(P)
f(x) = (m * (x - x0)) + y0
b: f(0)
u = Vector(P, R)
v = Vector(R, Q)
Steigungsdreieck, q, p, r = Polygon(P, R, Q)
schrittweite: 1
KorrekturPosTextSchrittweite = If(m ≥ 0, (0.2 | -0.2), (0.2 | 0.7))
KorrekturPosTextZuwachs = If(m ≥ 0, (0.2 | 0.4), (0.2 | 0))
mKlammer = If(m ≥ 0, LaTeX[m], "(" + (LaTeX[m]) + ")")
bKlammer = If(b ≥ 0, LaTeX[b], "(" + (LaTeX[b]) + ")")
a = Slope(f)
dx: x(Q) - x(P)
dy: y(Q) - y(P)
TextSchrittweite: "\Delta x = " + (LaTeX[dx]) + ""
TextZuwachs: "\Delta y = " + (LaTeX[dy])
P1: P + (1 | 0)
Q1: P1 + (0 | m)
w = Vector(P1, Q1)
h(x) = floor(x) - x
laengeP(x) = If[x ≥ 0, If[h(x) ≟ 0, 1, If[h((10 * x)) ≟ 0, 2.5, If[h((100 * x)) ≟ 0, 3.5]]]]
laenge(x) = If[x ≥ 0, If[h(x) ≟ 0, 1, If[h((10 * x)) ≟ 0, 2.5, If[h((100 * x)) ≟ 0, 3.5]]], If[h(x) ≟ 0, 2, If[h((10 * x)) ≟ 0, 3.6, If[h((100 * x)) ≟ 0, 4.5]]]]
mLaenge: laenge(round(m, 2))
ky = If(mLaenge ≟ 1, 0.1, If[mLaenge ≟ 2.5, 0.22, If[mLaenge ≟ 3.5, 0.32, If[mLaenge ≟ 2, 0.2, If[mLaenge ≟ 4.5, 0.43, 0.34]]]])
KorrekturPosTextSteigung: (ky * (cos(120°) | sin(120°)))
Text2: "" + (LaTeX[m]) + ""
M: (B + C) / 2
d2, m_2, a_2, b_2 = Polygon(A, B, M)
Text3 = RotateText(Text2, 30°)
d1, c, a_1, b_1 = Polygon(A, B, C)
Z: (A + M) / 2 + (-0.2 | 0.3)
Text1: "f(x) = \color{blue}{\underbrace{ " + (LaTeX[mKlammer]) + " }_{m}} \color{black}{\cdot x +} \color{purple}{\underbrace{ " + (LaTeX[bKlammer]) + " }_{b}} "
PosZuwachs = If(x(Q) > x(P), If[m ≥ 0, R + (0.2 | 0.4), R + (0.2 | 0)], If[m ≥ 0, R + (-2 | -0.2), R + (-2 | 0.4)])
PosSchrittweite = If(x(Q) > x(P), If[m ≥ 0, P + (0.2 | -0.2), P + (0.2 | 0.7)], If[m ≥ 0, P + (-2 | 0.5), P + (-2 | -0.2)])
X_P: (x(P) | 0)
Y_P: (0 | y(P))
g = Segment(P, Y_P)
i = Segment(X_P, P)
X_Q: (x(Q) | 0)
Y_Q: (0 | y(Q))
j = Segment(X_Q, Q)
k = Segment(Q, Y_Q)
e = false