End Behavior Calculator

How to Use the End Behavior Calculator

Step 1: Enter the Leading Coefficient

Begin by locating the input field labeled Leading Coefficient. In this field, input the coefficient of the term with the highest degree in your polynomial function. Ensure the value you enter is a number, as it is required for the calculation. This value is crucial in determining the function’s end behavior.

Step 2: Enter the Degree of the Polynomial

Next, find the input field labeled Degree of Polynomial. Enter the highest power of the function in this field. Note that the degree must be at least 1 and should be entered as a whole number. This will help the calculator assess whether the function has an even or odd degree.

Step 3: Select the Type of Function

Locate the field labeled Type of Function. Here, you will be presented with a dropdown menu. Select either Polynomial Function or Rational Function, depending on the nature of your mathematical expression. Choosing the correct type is essential for accurate calculations of end behavior.

Step 4: Understanding the Result Fields

• Left End Behavior (as x → -∞): After completing the input fields, review the calculator’s output for the left end behavior of the function. This description tells you how the function behaves as x approaches negative infinity.
• Right End Behavior (as x → ∞): Similarly, examine the right end behavior result, which describes the function’s behavior as x approaches positive infinity.
• Behavior Description: Lastly, read the detailed description field, which succinctly summarizes whether the polynomial is U-shaped, whether it opens upward or downward, or whether it conforms to another characteristic behavior.

By following these steps, you can effectively use the End Behavior Calculator to determine the asymptotic behavior of polynomial and rational functions based on their leading coefficients and degrees.