SOLUTION: Describe the vertical asymptote(s) and hole(s) for the graph of y=(x+2)(x+4)/(x+4)(x+1).

Question 844729: Describe the vertical asymptote(s) and hole(s) for the graph of y=(x+2)(x+4)/(x+4)(x+1).
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
For , does not exist, because the denominator is zero.
However, for any ,
which is continuous at .
So, at we have a hole in the graph.
The function is what results from "plugging" that hole.
For , does not exist, and there is no equivalent continuous function. (No plugging possible).
At , the functions and have a vertical asymptote.
The function changes sign at that point.
is positive for , where and .
It is negative for , where and .

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