Question

Math

Posted 2 months ago

```
Consider the graph of function $g$. The dashed lines represent asymptotes.
Find the limits of $g$ at negative and positive infinity.
$\begin{array}{l}
\lim _{x \rightarrow-\infty} g(x)= \\
\lim _{x \rightarrow \infty} g(x)=
\end{array}$
```

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Answer from Sia

Posted 2 months ago

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.

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