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

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

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Given:


y=((x+2)(x+4))/((x+4)(x+1))

Required:

We need tofnind the vertical asymptote(s) and hole (s) for the graph of the given function.

Step-by-step 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)


(x+4)(x+1)=0


(x+4)=0\text{ or }(x+1)=0
x=-4\text{ or x=-1}

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

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