Given:
[tex]y=\frac{(x+2)(x+4)}{(x+4)(x+1)}[/tex]
Required:
We need tofnind the vertical asymptote(s) and hole (s) for the graph of the given function.
Explanation:
Vertical asymptotes can be found when the numerator of the function is equal to zero.
The numerator of the given function is (x+4)(x+1)
[tex](x+4)(x+1)=0[/tex]
[tex](x+4)=0\text{ or }(x+1)=0[/tex][tex]x=-4\text{ or x=-1}[/tex]
The asymptote of the given function is either x =-4 or x =-1.
Recall that a hole exists on the graph of a rational function when both the numerator and denominator of the function are equal to zero.
The common factor of the given rational function
