Math Problem Statement

Which answer is correct?

What is the end behavior of the graph?

Solution

The question asks about the end behavior of the graph shown, with multiple choices. Let's analyze the graph and find the correct answer.

Observing the Graph:

  • On the left side, as xx \to -\infty, the graph appears to decrease, with yy \to -\infty.
  • On the right side, as xx \to \infty, the graph also decreases with yy \to -\infty.

Matching this with the provided answer choices:

The correct option is:

  • As xx \to -\infty, yy \to \infty and as xx \to \infty, yy \to -\infty

This matches the downward trend of the graph on both ends.

Would you like further details or have any questions about end behavior?

Here are five related questions to consider:

  1. How is the end behavior of a polynomial function determined?
  2. What does the degree of a polynomial tell you about its end behavior?
  3. How can you analyze the end behavior of a rational function?
  4. What is the impact of leading coefficient on the end behavior?
  5. How does symmetry (odd vs even functions) influence end behavior?

Tip: Always check the highest degree term in a function to predict its end behavior.

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Math Problem Analysis

Mathematical Concepts

End Behavior
Graph Analysis

Formulas

-

Theorems

End Behavior of Polynomial Functions

Suitable Grade Level

Grades 9-12