Question

Math

Posted 6 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 6 months ago

Solution by Steps

step 1

To find the limit of $g(x)$ as $x$ approaches negative infinity, we observe the behavior of the graph on the left side. The graph of $g(x)$ starts horizontally at approximately $y = 4$ and then approaches negative infinity as it nears the dashed line at $x = -3$. Therefore, $\lim_{x \rightarrow -\infty} g(x) = 4$

step 2

To find the limit of $g(x)$ as $x$ approaches positive infinity, we observe the behavior of the graph on the right side. The graph of $g(x)$ comes from positive infinity along the dashed line at $x = -3$ and then becomes mostly horizontal near $y = 1$. Therefore, $\lim_{x \rightarrow \infty} g(x) = 1$

Answer

$\lim_{x \rightarrow -\infty} g(x) = 4$ and $\lim_{x \rightarrow \infty} g(x) = 1$

Key Concept

Limits at infinity

Explanation

The limits at infinity describe the behavior of the function as $x$ approaches very large positive or negative values. In this case, the graph shows horizontal asymptotes indicating the function's values as $x$ goes to negative and positive infinity.

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