Question

Describe the vertical asymptotes) and hole(s) for the graph of y=x+2/x^2+8x+15

Answer 1

The answer is asymptotes: x=-5, x=-3 and no holes

Answer 2

• vertical asymptotes at x ∈ {-3, -5}
• no holes

Explanation:

We assume you intend your equation to be ...

... y = (x +2)/(x² +8x +15) = (x +2)/((x +3)(x +5))

This equation defines y everywhere except at x=-3 and x=-5, where there are vertical asymptotes. Because y is defined everywhere else, there are no holes.

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Comment on holes

A "hole" generally occurs when there is a numerator factor that cancels a denominator factor. Though the function has a removable discontinuity at that point, it is undefined where the (canceled) denominator factor is zero.