Non-permissible values are numbers that would cause the denominator to equal zero. Since it’s impossible to divide by zero, these numbers must be excluded.
They will however give 2 different types of breaks in the graph. If a factor like x – 2 occurs only in the denominator, then there is a vertical asymptote at x = 2. As the graph approaches closely to x = 2, it will shoot up or down toward ±∞. If the factor (x – 2) occurs in BOTH the numerator and denominator, there will not be an asymptote, but instead there will be a hole in the graph when x = 2. The graph is a continuing graph on each side of the hole. Nothing shoots toward infinity.
I hope that helps!! 🙂