6. find any points of discontinuity for the rational function. y = x-8/x^2 +6x-7 (1 point) x = 1, x = 7 x = 8 x = 1, x = –7 x = –1, x = 7 7. describe the vertical asymptote(s) and hole(s) for the graph of y = x-5/x^2 +4x +3 asymptotes: x = –3, –1 and no holes. asymptote: x = –3 and hole: x = –5 asymptotes: x = –3, –1 and hole: x = –5 asymptote: x = –5 and hole: x = –3 8. find the horizontal asymptote of the graph of y = -4x^6 +6x +3/8x^6 +9x+3 (1 point) y = 1 y = –1/2 y = 0 there is no horizontal asymptote.

6) Points of discontinuity of a rational function are those points where the denominator is equal to zero. 
Therefore you need to solve the equation:
x² + 6x - 7 = 0
(x + 7)(x - 1) = 0
x = -7 and x = -1 are points of discontinuity

7) Vertical asymptotes are found at those points where the denominator is equal to zero, holes are found at those points where both numerator and 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 asymptotes.

8) In order to find a horizontal asymptote, you need to look at the degree of both numerator and denominator and they must be equal to each other.
In your case, both degrees are 6, therefore you have a horizontal asymptote.
In order to find which line is the horizontal asymptote, you need to divide the coefficients of the highest degree monomials: -4/8 = -1/2. Therefore your horizontal asymptotes is y = -1/2

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