Answer
x-intercept: NONE
y-intercept: (0, -1)
Vertical Asymptote: x=6, -1
Domain: (-∞, -1) U (-1, 6) U (6, ∞)
Horizontal Asymptote: y=0
Range: (-∞, 0) U (0, ∞)
See graph below
Work Step by Step
$r(x)=\frac{6}{x^2 - 5x - 6}$
No x-intercept, numerator acan never be equal to zero
y-intercept is the ratio of the constants, which is 6 / -6 = -1
Thus, the y-intercept is at (0, -1)
Vertical asymptotes are when the denominator is equal to 0
$(x^2 - 5x - 6) = 0$
$(x-6)(x+1) = 0$
x = 6, -1
So, domain is from (-∞, -1) U (-1, 6) U (6, ∞)
Horizontal asymptote is the ratio of the constants of the leading term (with equal degree)
0 (since top degree is not 2, unlike bottom)
Thus, the horizontal asymptote is at y=0
So the range is from (-∞, 0) U (0, ∞)