Explanation:
to create a vertical asymptote (a tangent of the curve in infinity) at x = n we define e.g.
f(x) = 1/(x - n)
the cost x gets to n, the much closer the function gets to 1/0 and infinity.
so, the part to get us the asymptote at x = -4 is
1/(x + 4)
the part to get us the asymptote at x = 2 is
1/(x - 2)
and the part that gives us a zero solution at x = 3 is
(x - 3)
because that is what the point (3, 0) is : when x = 3. then y = 0.
now we only need to multiply all 3 parts to combine them :
f(x) = 1/(x + 4) × 1/(x - 2) × (x - 3)