Subjects algebra

Vertical Asymptote 2C1D07

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1. The problem is to identify the vertical asymptote (VA) and the possible presence of a horizontal or oblique (slant) asymptote (CA) for a function with denominator $x+1$. 2. A vertical asymptote occurs where the denominator of a rational function is zero and the numerator is not zero at that point. Here, the denominator is $x+1$. 3. Set the denominator equal to zero to find the VA: $$x+1=0$$ $$x=-1$$ This means there is a vertical asymptote at $x=-1$. 4. The vertical asymptote is represented on the graph as a dotted vertical line at $x=-1$. 5. To check for a horizontal or oblique asymptote (CA), consider the degrees of the numerator and denominator: - If the degree of numerator $<$ degree of denominator, horizontal asymptote is $y=0$. - If degrees are equal, horizontal asymptote is ratio of leading coefficients. - If degree numerator $>$ degree denominator by 1, oblique asymptote exists. 6. Since the user only mentioned the denominator $x+1$ and no numerator, we cannot determine the CA without more information. Final answer: The vertical asymptote is at $x=-1$, shown as a dotted line on the graph. The presence of a horizontal or oblique asymptote depends on the numerator and cannot be confirmed here.