Answer: D
Step-by-step explanation:
[tex]f(x) = \dfrac{2}{x-1}-3[/tex]
The vertical asymptote is the restriction on the x-value. Since the denominator cannot be equal to zero, then x - 1 ≠ 0 → x ≠ 1. So, the vertical asymptote is: x = 1
The horizontal asymptote is the restriction on the y-value. Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. However, there is a vertical shift of 3 units down so the horizontal asymptote is: y = -3
The only graph that has these asymptotes is the last one, which I call graph D.
