91ed68…: “Except a careful lemma”

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Let $L(z) = -\log _3(5-z) + 1$ with its natural domain.

The graph of $y = L(z)$ is to the left right of the vertical asymptote $z = 5$.

The domain of $y = L(z)$ is

\[ \left ( \answer {-\infty }, \answer {5} \right ) \]

$L(z)$ is an increasing decreasing function.

\[ \lim \limits _{z \to 5^-} L(z) = \answer {\infty } \]

\[ \lim \limits _{z \to -\infty } L(z) = \answer {-\infty } \]

2025-05-17 23:55:08