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Describe the vertical asymptote(s) and hole(s) for the graph of y= (x+2) / (x^2+8x+15).a) asymptotes: x = 3 and 5 and hole: x = - 2b) asymptotes: x = 3 and 5 and no holesc) asymptotes: x = - 5, - 3 and hole: x = - 2d) asymptotes: x = - 5, - 3 and no holes

Respuesta :

we have the function

[tex]y=\frac{x+2}{x^2+8x+15}[/tex]

Simplify

[tex]x^2+8x+15=(x+5)(x+3)[/tex]

substitute

[tex]y=\frac{x+2}{(x+5)(x+3)}[/tex]

Remember that

The denominator cannot be equal to zero

so

The domain of the given function, are all real numbers, except for x=-5 and x=-3

that means

There are vertical asymptotes at x=-5 and at x=-3

No holes in the graph

therefore

The answer is the option D

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