Consider the graph of function $g$. The dashed lines represent asymptotes.

Find the limits of $g$ at negative and positive infinity.
$$
\begin{array}{l}
\lim _{x \rightarrow-\infty} g(x)= \
\lim _{x \rightarrow \infty} g(x)=
\end{array}
$$

Question

Consider the graph of function $g$. The dashed lines represent asymptotes.

Find the limits of $g$ at negative and positive infinity.
$$
\begin{array}{l}
\lim _{x \rightarrow-\infty} g(x)= \
\lim _{x \rightarrow \infty} g(x)=
\end{array}
$$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the limit of $g(x)$ as $x$ approaches $-\infty$, we observe the behavior of the graph in the leftmost part. The graph starts slightly above the dashed horizontal line at $y = 3$ and approaches this line as $x$ goes to $-\infty$. Therefore, $ \lim_{x \rightarrow -\infty} g(x) = 3 $. ‖ ‖ step 2 ⋮ To find the limit of $g(x)$ as $x$ approaches $\infty$, we observe the behavior of the graph in the rightmost part. The graph approaches the dashed horizontal line at $y = 1$ as $x$ goes to $\infty$. Therefore, $ \lim_{x \rightarrow \infty} g(x) = 1 $. ‖ ∻Answer∻ ⚹ $$ \lim_{x \rightarrow -\infty} g(x) = 3 \ \lim_{x \rightarrow \infty} g(x) = 1 $$ ⚹ ∻Key Concept∻ ⚹Limits of a function as $x$ approaches $-\infty$ and $\infty$⚹ ∻Explanation∻ ⚹The limits of a function as $x$ approaches $-\infty$ and $\infty$ can be determined by observing the behavior of the graph near the horizontal asymptotes.⚹◊What techniques can be used to estimate limits using tables for the given function $g(x)$?⍭ Generate me a similar question◊

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