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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 X2 X4 X4 X1 class=

Sagot :

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