Author: המרכז הארצי למורים למתמטיקה בחינוך העל יסודי
Date: 2013 ‎מאי‎ 2

What feature on the graph corresponds with the a value? The b value? c? d?
The graph typically has three "branches." What causes one branch to collide with and then re-separate from its neighboring branch?
Use the vocabulary of discontinuities to describe what you see.
Is it possible to create more than two discontinuities for this function? If so, what is the maximum number of discontinuities?
Is it possible to create less than two discontinuities for this function? If so, what is the minimum number of discontinuities?

jeromeAwhite

h(x)=\frac{(x-a)(x-b)}{(x-c)(x-d)}

''חורים'' ואסימפטוטות בפונקציה רציונאלית

a = 0 (slider from -5 to 5, step 0.1)
b = 2 (slider from -5 to 10, step 0.1)
d = -1 (slider from -5 to 5, step 0.1)
c = 3 (slider from -5 to 10, step 0.1)
g(x) = (x - c) * (x - d)
f(x) = (x - a) * (x - b)
h(x) = f(x) / g(x)
e: x = c
i: x = d
text1: "h(x) = " + (LaTeX[h]) + ""
A_1 = If(a ≟ b ∧ b ≟ c ∧ c ≟ d, (a, 1), If[c ≟ a, (c, (c - b) / (c - d)), If[c ≟ b, (c, (c - a) / (c - d)), (0, 0)]])
B: A_1
h_1: h
A' = If(d ≟ a, (d, (d - b) / (d - c)), If[d ≟ b, (d, (d - a) / (d - c)), (0, 0)])
B': A'
A = Point(h)