f(x)

V.

H.

Numerador

Denominador

Eje x

Eje y

Asíntotas

O.

Cortes con ejes

Extremos relativos

Punto sobre f(x)

2

3

4

5

+

+

+

+

+

+

-

-

-

-

-

-

1

Acerca

Aleja

f(x)=\frac{ax^2+bx+c}{a'x^2+b'x+c'}

c' = 0 (slider from -6 to 6, step 1)
b' = 1 (slider from -6 to 6, step 1)
a' = 0 (slider from -6 to 6, step 1)
d(x) = (a' * x^(2)) + (b' * x) + c'
q = Simplify(d)
a = 0 (slider from -6 to 6, step 1)
b = 0 (slider from -6 to 6, step 1)
c = 4 (slider from -6 to 6, step 1)
f_1(x) = ((a * x^(2)) + (b * x) + c) / ((a' * x^(2)) + (b' * x) + c')
f = Simplify(f_1)
asv: false
lista1: {}
n(x) = (a * x^(2)) + (b * x) + c
ash: false
texto1: "f(x)=" + (LaTeX[f_1]) + "=" + (LaTeX[f]) + ""
corx: false
cory: false
as = false
aso: false
cor = false
r = Div(n, d)
s = Degree(d)
i = false
j = false
k = false
gd = Degree(q)
p = Simplify(n)
gn = Degree(p)
P = Point(f_1)
v = false
b_1 = false
texto4: "f(x)=" + (LaTeX[f]) + ""
lista2 = Asymptote(f)
C = Intersect(f_1, yAxis, (0, -4))
A, B = Intersect(p, xAxis)
der1(x) = ((((2 * a) * x) + b) * q(x)) - ((((2 * a') * x) + b') * p(x))
m = Simplify(der1)
E1, E2 = Root(m)
j_1 = OrthogonalLine(E2, xAxis)
k_1 = OrthogonalLine(E1, xAxis)
E' = Intersect(f_1, j_1, (2, 4))
E = Intersect(f_1, k_1, (-2, -4))
g(x) = (m'(x) * q(x)^(2)) - ((2 * q(x)) * m(x))
p_1(x) = (m'(x) * q(x)) - ((2 * m(x)) * q'(x))
q_1 = Simplify(p_1)
F, G, I_1 = Root(q_1)
l = OrthogonalLine(G, xAxis)
l_1 = OrthogonalLine(I_1, xAxis)
K1, N, O = Intersect(q_1, xAxis)
n_1 = OrthogonalLine(F, xAxis)
o: false
a_1: false
texto5: "" + (LaTeX[lista2]) + ""