Answer :
Given:-
Investigate several functions.
To find the similarites and differences.
So now we assume the functions,
[tex]\frac{x+1}{x-1},\frac{x-1}{2x}[/tex]now we substitute the value of 1 for x. so we get,
[tex]\begin{gathered} \frac{x+1}{x-1}=\frac{1+1}{1-1}=\frac{2}{0} \\ \frac{x-1}{2x}=\frac{1-1}{2(1)}=\frac{0}{2} \end{gathered}[/tex]So in these two cases at first case the value of 2/0 will become infinity and there comes a hole in the graph.
But in the second case the value of 0/2 will become zero and there will not be any hole in the graph.
Like this there comes some changes between each function.