QuestionAugust 25, 2025

6. Write an equation of a function, g(x) where lim _(xarrow 2)g(x)=-infty and a horizontal asymptote of y=0

6. Write an equation of a function, g(x) where lim _(xarrow 2)g(x)=-infty and a horizontal asymptote of y=0
6. Write an equation of a function, g(x) where lim _(xarrow 2)g(x)=-infty and a horizontal asymptote of y=0

Solution
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Answer

g(x) = -\frac{1}{(x-2)^2} Explanation 1. Define the function with a vertical asymptote Choose g(x) = \frac{1}{(x-2)^2}, which has a vertical asymptote at x=2. 2. Ensure horizontal asymptote at y=0 As x \to \pm\infty, \frac{1}{(x-2)^2} \to 0. Thus, y=0 is a horizontal asymptote.

Explanation

1. Define the function with a vertical asymptote<br /> Choose $g(x) = \frac{1}{(x-2)^2}$, which has a vertical asymptote at $x=2$.<br />2. Ensure horizontal asymptote at $y=0$<br /> As $x \to \pm\infty$, $\frac{1}{(x-2)^2} \to 0$. Thus, $y=0$ is a horizontal asymptote.
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