What is End Behavior?

End behavior refers to the behavior of a polynomial function as the input variable (usually x) approaches positive or negative infinity. It describes how the function’s output (y) changes as x gets very large in either the positive or negative direction. Understanding end behavior is crucial for graphing polynomials and analyzing their long-term trends.

How to Use the End Behavior Calculator

Step 1: Enter the polynomial function

Type your polynomial function into the input field. Use standard algebraic notation, with “x” as the variable and “^” for exponents. For example, enter “2x^3 – 4x^2 + 5x – 1” for the function 2x³ – 4x² + 5x – 1.

Step 2: Click the “Calculate End Behavior” button

After entering your function, click the blue “Calculate End Behavior” button. The calculator will process your input and determine the end behavior.

Step 3: Interpret the results

The calculator will display the end behavior result and provide a brief explanation. The result shows how the function behaves as x approaches positive and negative infinity, using arrow notation (→).

Step 4: Read the explanation

Below the result, you’ll find an explanation of why the function behaves this way. This explanation considers the degree of the polynomial and the sign of the leading coefficient.

Step 5: Analyze different functions

You can repeat the process with different polynomial functions to compare their end behaviors. This can help you understand patterns in polynomial behavior based on their degrees and leading coefficients.

Step 6: Use the results for further analysis

Apply the end behavior information to sketch graphs, predict long-term trends, or solve more complex problems involving polynomial functions.