Answer: The Horizontal asymptote of f(x) and g(x) is y=0. The third option is correct.
Explanation:
it is given that the using the rules of transformations to compare the graphs of the functions,
[tex]f(x)=\frac{1}{x}[/tex]
[tex]g(x)=\frac{5}{x-1}[/tex]
The graph of f(x) vertically stretch by factor 5 and shifts 1 unit right to transform g(x).
To find vertical asymptotes equate denominator equal to 0.
[tex]x=0[/tex]
[tex]x=1[/tex]
Therefore the function f(x) has vertical asymptote x=0, and g(x) has vertical asymptote x=1. So their is not common vertical asymptote.
To find horizontal asymptotes put [tex]x=\infty[/tex].
[tex]f(x)\rightarrow 0\text{ as }x\rightarrow \infty[/tex]
[tex]g(x)\rightarrow 0\text{ as }x\rightarrow \infty[/tex]
Therefore, the function have common horizontal asymptote, i.e., y=0.
