Question

use the graph of the rational function to complete the following statement.

as \\(x \
ightarrow -\infty\\), \\(f(x) \
ightarrow \underline{\quad\quad}\\)

as \\(x \
ightarrow -\infty\\), \\(f(x) \
ightarrow \square\\)

Explanation:

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<reasoning>

Identify the target behavior

Using the Rational Function End Behavior knowledge point
\[
\text{Find } \lim_{x \to -\infty} f(x)
\]

Analyze the graph's left end

Using the Horizontal Asymptotes knowledge point
\[

$$\begin{aligned} &\text{As } x \to -\infty, \text{ the curve approaches the horizontal line } y = 1.\\ &\text{Thus, } f(x) \to 1. \end{aligned}$$

\]
</reasoning>

<answer>
As \(x \to -\infty\), \(f(x) \to\) <blank>1</blank>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
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"Mathematics",
"Algebra",
"Rational Function End Behavior"
]
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Answer:

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</pre_analysis>

<reasoning>

Identify the target behavior

Using the Rational Function End Behavior knowledge point
\[
\text{Find } \lim_{x \to -\infty} f(x)
\]

Analyze the graph's left end

Using the Horizontal Asymptotes knowledge point
\[

$$\begin{aligned} &\text{As } x \to -\infty, \text{ the curve approaches the horizontal line } y = 1.\\ &\text{Thus, } f(x) \to 1. \end{aligned}$$

\]
</reasoning>

<answer>
As \(x \to -\infty\), \(f(x) \to\) <blank>1</blank>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Rational Function End Behavior"
]
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