$Step%v$

$O$

f(x)=2^x

(1,2)

(2,4)

(3,8)

(0,1)

(-1,\frac{1}{2})

(-2,\frac{1}{4})

(-3,\frac{1}{8})

g(x)=2^{-x}=\frac{1}{2^x}

h(x)=-2^x

k(x)=-2^{-x}

$a=%v$

Reset

x

y

指數函數的圖形(1)

n = 0 (slider from 0 to 20, step 1)
t2 = 0 (slider from 0 to 1, step 0.01)
O = (12.552445796491757, -11.081818320771477)
Q_2: (0.7 * Corner[2]) + (0.3 * Corner[1])
Q_3: (x(Q_2), y(Corner[3]))
side = Segment(Q_2, Q_3)
A_1: O + (t2 * Vector[O, (x(Q_2), y(O))])
B_1: O + (t2 * Vector[O, (x(O), y(Q_3))])
A_2: O + (t2 * Vector[O, (x(Corner[1]), y(O))])
B_2: O + (t2 * Vector[O, (x(O), y(Corner[2]))])
u_1 = Vector(O, A_1)
u_2 = Segment(O, A_2)
v_1 = Vector(O, B_1)
v_2 = Segment(O, B_2)
A_4: O + (1, 2)
A_5: O + (2, 4)
A_6: O + (3, 8)
A_7: O + (0, 1)
A_8: O + (-1, 1 / 2)
A_9: O + ((-2), 1 / 4)
A_{10}: O + ((-3), 1 / 8)
f(x) = 2^(x - x(O)) + y(O)
list11 = Sequence((k, 2^(k)) + O, k, -20, round(x(Q_2)), 0.25)
t12 = 5.158625864318857 (slider from x(Corner[1]) to x(Q_2), step 0.01)
g(x) = 2^((-x) + x(O)) + y(O)
f_{14}(x) = If[x(Corner[1]) ≤ x ≤ x(Q_2),g(x)]
f_{16}(x) = (-2^(x - x(O))) + y(O)
k(x) = (-2^((-x) + x(O))) + y(O)
f_{18}(x) = If[x(Corner[1]) ≤ x ≤ x(Q_2),k(x)]
a = 2 (slider from 0.1 to 5, step 0.1)
p(x) = a^(x - x(O)) + y(O)
f_{19}(x) = If[x(Corner[1]) ≤ x ≤ x(Q_2),p(x)]
text19: "f(x)=" + (LaTeX[a]) + "^x"
f_{12}(x) = If[x(Corner[1]) ≤ x ≤ t12,f(x)]