THIS USER ASKED 👇
Find any points of discontinuity for the rational function y=x-8/x^2+5x-6
THIS IS THE BEST ANSWER 👇
6) Discontinuity points are a rational function of those points where the denominator is equal to zero.
Therefore you must solve the equation:
x² + 6x – 7 = 0
(x + 7) (x – 1) = 0
X = -7 and x = 11 are points of discontinuity
7) Vertical asymmetries are found at those points where the denominator is equal to zero, holes are found at those points where both the numerator and the denominator are equal to zero at the same time.
Therefore you need to solve two equations:
x – 8 = 0
x = 8
x² + 4x + 3 = 0
(x + 3) (x + 1)
x = -3 and x = -1
Therefore, you have no holes and x = -3 and x = -1 are vertical asymmetries.
8) To get a horizontal asymptote, you need to look at both the numerator and denominator level and they must be equal.
In your case, both steps are 6, so you have a horizontal asymptote.
In order to determine which line is the horizontal asymptote, you need to divide the coefficients of the highest degree monomers: -4/8 = -1/2. Thus y = -1/2 for horizontal asymptotes
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