Question

Based on the table, which best predicts the end behavior of the graph of f(x)?

As x → ∞, f(x) → ∞, and as x → –∞, f(x) → ∞.
As x → ∞, f(x) → ∞, and as x → –∞, f(x) → –∞.
As x → ∞, f(x) → –∞, and as x → –∞, f(x) → ∞.
As x → ∞, f(x) → –∞, and as x → –∞, f(x) → –∞.

Answer 1

To determine the end behavior of the function \( f(x) \), we need to analyze the values that \( f(x) \) approaches as \( x \) goes to \( \infty \) (positive infinity) and \( -\infty \) (negative infinity).

Here’s a summary of the options given:

1. As \( x \to \infty \), \( f(x) \to \infty \)
and as \( x \to -\infty \), \( f(x) \to \infty \).

2. As \( x \to \infty \), \( f(x) \to \infty \)
and as \( x \to -\infty \), \( f(x) \to -\infty \).

3. As \( x \to \infty \), \( f(x) \to -\infty \)
and as \( x \to -\infty \), \( f(x) \to \infty \).

4. As \( x \to \infty \), \( f(x) \to -\infty \)
and as \( x \to -\infty \), \( f(x) \to -\infty \).

Given that I cannot see the specifics of your table, I can explain how to analyze the end behavior typically:

- For even degree polynomials, the end behavior tends to be the same in both directions (either both \( \infty \) or both \( -\infty \)).
- For odd degree polynomials, the end behavior will differ (one direction will go to \( \infty \) and the other to \( -\infty \)).
- Rational functions can behave differently based on their degree and leading coefficients.

You would need to refer to the specifics of the function described in the table to choose the correct option based on its end behavior patterns. If you have more context or the type of function, I can provide a more definitive answer!