Questions: Which of the following notations correctly describe the end behavior of the polynomial graphed below? A. x → -∞, f(x) → -∞ x → ∞, f(x) → ∞ B. x → -∞, f(x) → ∞ x → ∞, f(x) → ∞ C. x → -∞, f(x) → ∞ x → ∞, f(x) → -∞ D. x → -∞, f(x) → -∞ x → ∞, f(x) → -∞

Which of the following notations correctly describe the end behavior of the polynomial graphed below? A. x → -∞, f(x) → -∞ x → ∞, f(x) → ∞ B. x → -∞, f(x) → ∞ x → ∞, f(x) → ∞ C. x → -∞, f(x) → ∞ x → ∞, f(x) → -∞ D. x → -∞, f(x) → -∞ x → ∞, f(x) → -∞
Transcript text: Which of the following notations correctly describe the end behavior of the polynomial graphed below? A. $x \rightarrow-\infty, f(x) \rightarrow-\infty$ $x \rightarrow \infty, f(x) \rightarrow \infty$ B. $x \rightarrow-\infty, f(x) \rightarrow \infty$ $x \rightarrow \infty, f(x) \rightarrow \infty$ C. $\begin{array}{l}x \rightarrow-\infty, f(x) \rightarrow \infty \\ x \rightarrow \infty, f(x) \rightarrow-\infty\end{array}$ D. $x \rightarrow-\infty, f(x) \rightarrow-\infty$ $x \rightarrow \infty, f(x) \rightarrow-\infty$
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Solution

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Solution Steps

Step 1: Analyze the graph's behavior as x approaches negative infinity.

As we move left along the x-axis (x → -∞), the graph extends upwards, meaning f(x) approaches positive infinity (f(x) → ∞).

Step 2: Analyze the graph's behavior as x approaches positive infinity.

As we move right along the x-axis (x → ∞), the graph extends downwards, meaning f(x) approaches negative infinity (f(x) → -∞).

Step 3: Match the behavior with the given options.

The behavior we observed is described by option C: x → -∞, f(x) → ∞ and x → ∞, f(x) → -∞.

Final Answer

C

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