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Question
Math
Posted 2 months ago

Consider the graph of function gg. The dashed lines represent asymptotes.

Find the limits of gg at negative and positive infinity.
limxg(x)=limxg(x)=
\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)g(x) as xx approaches -\infty, we observe the behavior of the graph in the leftmost part. The graph starts slightly above the dashed horizontal line at y=3y = 3 and approaches this line as xx goes to -\infty. Therefore, limxg(x)=3 \lim_{x \rightarrow -\infty} g(x) = 3
step 2
To find the limit of g(x)g(x) as xx approaches \infty, we observe the behavior of the graph in the rightmost part. The graph approaches the dashed horizontal line at y=1y = 1 as xx goes to \infty. Therefore, limxg(x)=1 \lim_{x \rightarrow \infty} g(x) = 1
Answer
limxg(x)=3limxg(x)=1 \lim_{x \rightarrow -\infty} g(x) = 3 \\ \lim_{x \rightarrow \infty} g(x) = 1
Key Concept
Limits of a function as xx approaches -\infty and \infty
Explanation
The limits of a function as xx approaches -\infty and \infty can be determined by observing the behavior of the graph near the horizontal asymptotes.

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