Answer:
See below for answers and explanations (as well as a graph attached)
Step-by-step explanation:
The function [tex]f(x)=\frac{x-5}{x^2-1}[/tex] can be written as [tex]\frac{x-5}{(x+1)(x-1)}[/tex], showing that there are 2 vertical asymptotes, which are at [tex]x=-1[/tex] and [tex]x=1[/tex] as they both make the denominator equal to 0.
Additionally, there would be a horizontal asymptote at [tex]y=0[/tex] since the degree of the numerator is less than the degree of the denominator.
See the attached graph.
