Answer:
To find the x and y intercepts, we set x and y to zero respectively:
x-intercept: setting y = 0 gives us 6/(x^2 - 5x - 6) = 0, which has no real solutions.
y-intercept: setting x = 0 gives us s(0) = 6/(-6) = -1.
To find the vertical asymptotes, we set the denominator equal to zero and solve for x:
x^2 - 5x - 6 = 0
(x - 6)(x + 1) = 0
This gives us two vertical asymptotes at x = 6 and x = -1.
To find the horizontal asymptote, we need to look at the behavior of the function as x approaches infinity and negative infinity. As x becomes very large in magnitude, the terms involving x^2 become much larger than the terms involving x or the constant term, and so we can ignore those terms. This gives us:
s(x) ≈ 6/x^2 as x → ±∞
Therefore, the horizontal asymptote is y = 0.
In summary:
x-intercept: none
y-intercept: (0, -1)
vertical asymptotes: x = 6 and x = -1
horizontal asymptote: y = 0
If you have anymore questions, feel free to comment and I will answer them 8-5 I am on.
Explanation: