Author: Judah L. Schwartz

Select a form for f(x). Explore how the graph depends on the parameters a, b and c. How does the expression for f(x) vary as you translate and/or scale its graph?

Select a form for g(x) and an operation to combine f(x) and g(x). See the written statement of the challenge for questions to think about as you explore this app.

Scale_g ∧ ∨

Scale_g > <

Translate_g  ∨ ∧

Translate_g > <

Scale_f ∨ ∧

הזזה ימינה ושמאלה

ax + b

a|x - b| + c

ax² + bx + c

Ax² + Bx + C

A|x - B| + C

Ax + B

f(x) + g(x)

f(x) - g(x)

f(x) * g(x)

f(x) / g(x)

f(g(x))

g(x) - f(x)

g(x) / f(x)

g(f(x))

בחרו פונקציה אחת מכל טור  

בחרו פעולה

אתחול

פרופ' יהודה שוורץ
בעריכת מרכז המורים

בחרו פעולה

Scale_gUD = 1 (slider from 0.1 to 10, step 0.1)
Scale_gLR = 1 (slider from 0.1 to 10, step 0.1)
Translate_gUD = 0 (slider from -10 to 10, step 0.1)
Translate_gLR = 0 (slider from -10 to 10, step 0.1)
A = 1 (slider from -5 to 5, step 0.1)
B = 0 (slider from -5 to 5, step 0.1)
C = 0 (slider from -5 to 5, step 0.1)
Scale_fLR = 1 (slider from 0.1 to 10, step 0.1)
Translate_fUD = 0 (slider from -10 to 10, step 0.1)
c = 0 (slider from -5 to 5, step 0.1)
b = 0 (slider from -5 to 5, step 0.1)
a = 1 (slider from -5 to 5, step 0.1)
Scale_fUD = 1 (slider from 0.1 to 10, step 0.1)
Translate_fLR = 0 (slider from -10 to 10, step 0.1)
fL(x) = (a * (x * Scale_fLR - Translate_fLR) + b + Translate_fUD) * Scale_fUD
fQ(x) = (a * (x * Scale_fLR - Translate_fLR)^(2) + b * (x * Scale_fLR - Translate_fLR) + c + Translate_fUD) * Scale_fUD
fLinear = false
fAbsolute = false
fQuadratic = false
gL(x) = (A * (x * Scale_gLR - Translate_gLR) + B + Translate_gUD) * Scale_gUD
gQ(x) = (A * (x * Scale_gLR - Translate_gLR)^(2) + B * (x * Scale_gLR - Translate_gLR) + C + Translate_gUD) * Scale_gUD
gQuadratic = false
gAbsolute = false
gLinear = false
fA(x) = (a * abs(x * Scale_fLR - Translate_fLR - b) + c + Translate_fUD) * Scale_fUD
gA(x) = (A * abs(x * Scale_gLR - Translate_gLR - B) + C + Translate_gUD) * Scale_gUD
add = false
subtract = false
multiply = false
divide = false
compose = false
subtractgf = false
dividegf = false
composegf = false
f(x) = fLinear * fL(x) + fQuadratic * fQ(x) + fAbsolute * fA(x)
g(x) = gLinear * gL(x) + gQuadratic * gQ(x) + gAbsolute * gA(x)
h = If(add, f(x) + g(x))
p = If(compose, f(g(x)))
q = If(composegf, g(f(x)))
r = If(divide, f(x) / g(x))
t = If(multiply, f(x) * g(x))
f_1 = If(subtract, f(x) - g(x))
g_1 = If(subtractgf, g(x) - f(x))
s = If(dividegf, g(x) / f(x))
text9: "הזזה ימינה ושמאלה =" + Translate_fLR + ""
text10: "הזזה למעלה למטה = " + Translate_fUD + ""
text9_1: "הזזה ימינה ושמאלה =" + Translate_fLR + ""
text10_1: "הזזה למעלה למטה = " + Translate_fUD + ""
F = If(fLinear, fL, If[fQuadratic, fQ, fA])
text8: "f(x) = " + (Expand[F]) + " "
G = If(gLinear, gL, If[gQuadratic, gQ, gA])
text11: "g(x) = " + (Expand[G]) + ""
text7: "f(x)=" + F + ""
text14: "מתיחה ימינה ושמאלה = " + Scale_fLR + ""
text15: "מתיחה למעלה ולמטה = " + Scale_fUD + ""
text14_1: "מתיחה ימינה ושמאלה = " + Scale_gLR + ""
text15_1: "מתיחה למעלה ולמטה = " + Scale_gUD + ""
text2: "h(x)=" + (LaTeX[Expand[F(x) + G(x)]]) + ""
text1: "h(x)=" + (LaTeX[Expand[F(x) - G(x)]]) + ""
text6: "h(x)= \frac{" + (LaTeX[Expand[F]]) + "}{" + (LaTeX[Expand[G]]) + "}"
text4: "h(x)=" + (LaTeX[Expand[F(x) * G(x)]]) + ""
text13: "h(x)=" + (LaTeX[Expand[G(x) - F(x)]]) + ""
text17: "h(x)=" + (LaTeX[Expand[G(x) / F(x)]]) + ""
text12: "h(x)= " + (LaTeX[Expand[F(G(x))]]) + ""
text18: "h(x)=" + (Expand[G(F(x))]) + ""