Questions: Use the graph of the rational function to complete the following statement. As x → 4^+, f(x) → . As x → 4^+, f(x) → 4. Asymptotes are shown as dashed lines. The horizontal asymptote is y=-3. The vertical asymptotes are x=-1 and x=4.

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

As x → 4^+, f(x) → .

As x → 4^+, f(x) → 4.

Asymptotes are shown as dashed lines. The horizontal asymptote is y=-3. The vertical asymptotes are x=-1 and x=4.
Transcript text: Use the graph of the rational function to complete the following statement. \[ \text { As } x \rightarrow 4^{+}, f(x) \rightarrow \] $\qquad$ . $\qquad$ \[ \text { As } \mathrm{x} \rightarrow 4^{+}, \mathrm{f}(\mathrm{x}) \rightarrow 4 \text {. } \] Asymptotes are shown as dashed lines. The horizontal asymptote is $y=-3$. The vertical asymptotes are $\mathrm{x}=-1$ and $\mathrm{x}=4$.
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Solution

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Solution Steps

Step 1: Analyze the graph as x approaches 4 from the left

The question asks for the behavior of f(x) as x approaches 4 from the left (x → 4⁻). Looking at the graph, as the x-values get closer and closer to 4 from the left side, the function values appear to increase without bound.

Step 2: Express the behavior using limit notation

This unbounded increase is represented by ∞.

Final Answer: ∞

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