Subjects calculus

Vertical Asymptotes 15D30F

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1. The problem asks for the equations of the vertical asymptotes of the given graph. 2. Vertical asymptotes occur where the function approaches infinity or negative infinity as $x$ approaches a certain value. These are typically values where the function is undefined, often due to division by zero. 3. From the graph description, vertical asymptotes are near $x = -1$. 4. To confirm, check the behavior of the function as $x$ approaches $-1$ from the left and right: $$\lim_{x \to -1^-} y = \pm \infty, \quad \lim_{x \to -1^+} y = \pm \infty$$ 5. Since the function tends to infinity near $x = -1$, the vertical asymptote is at: $$x = -1$$ 6. No other vertical asymptotes are indicated by the graph description. Final answer: $$x = -1$$