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## Sagot :

We are given the following table:

[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & -5 & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline f(x) & 14 & 6 & 0 & -4 & -6 & -6 & -4 & 0 & 6 \\ \hline \end{array} \][/tex]

### Step-by-Step Analysis

1.

**Understanding the Values at the Extremes:**

- For [tex]\( x = -5 \)[/tex], [tex]\( f(x) = 14 \)[/tex]

- For [tex]\( x = 3 \)[/tex], [tex]\( f(x) = 6 \)[/tex]

2.

**Behavior as [tex]\( x \)[/tex] Increases (Moving from Left to Right in the Table):**

- From [tex]\( x = -5 \)[/tex] to [tex]\( x = 0 \)[/tex], [tex]\( f(x) \)[/tex] decreases from 14 to -6.

- From [tex]\( x = 0 \)[/tex] to [tex]\( x = 3 \)[/tex], [tex]\( f(x) \)[/tex] increases from -6 to 6.

3.

**Observing the Pattern:**

- After reaching [tex]\( x = 0 \)[/tex], as [tex]\( x \)[/tex] increases further, [tex]\( f(x) \)[/tex] increases from -6 to a positive value (6).

- This indicates a potential trend towards positive values as [tex]\( x \to \infty \)[/tex].

4.

**Behavior as [tex]\( x \)[/tex] Decreases (Moving from Right to Left in the Table):**

- From [tex]\( x = 3 \)[/tex] to [tex]\( x = 0 \)[/tex], [tex]\( f(x) \)[/tex] decreases down to -6.

- From [tex]\( x = 0 \)[/tex] to [tex]\( x = -5 \)[/tex], [tex]\( f(x) \)[/tex] increases back up to 14.

5.

**Conclusion on End Behavior:**

- As [tex]\( x \to \infty \)[/tex], based on the increasing trend from [tex]\( x = 0 \)[/tex] to [tex]\( x = 3 \)[/tex] and the overall pattern, [tex]\( f(x) \)[/tex] appears to move towards positive infinity.

- As [tex]\( x \to - \infty \)[/tex], based on the increasing trend seen when moving back towards negative [tex]\( x \)[/tex]-values, it suggests that [tex]\( f(x) \)[/tex] also tends to positive infinity.

Based on the observed pattern from the table values, we can conclude that:

- As [tex]\( x \rightarrow \infty, f(x) \rightarrow \infty \)[/tex]

- As [tex]\( x \rightarrow - \infty, f(x) \rightarrow \infty \)[/tex]

Therefore, the best statement that describes the end behavior of the graph of [tex]\( f(x) \)[/tex] is:

"As [tex]\( x \rightarrow \infty, f(x) \rightarrow \infty, and as \( x \rightarrow - \infty, f(x) \rightarrow \infty \)[/tex]."

This corresponds to option:

**2.**[tex]\( \text{As } x \rightarrow \infty, f(x) \rightarrow \infty, \text{ and as } x \rightarrow -\infty, f(x) \rightarrow \infty \)[/tex].