Asymptote Calculator

Using the Asymptote Calculator

This guide will walk you through the process of using the Asymptote Calculator to analyze rational and square root functions. By following these steps, you can determine horizontal, oblique, and vertical asymptotes based on the attributes of the function you provide.

Step 1: Select Function Type

The first step involves selecting the type of function you will be analyzing. The calculator provides two options:

• Rational Function (f(x) = p(x)/q(x))
• Square Root Function

Select the appropriate option from the dropdown list labeled Function Type. Note that this guide focuses on rational functions, as the calculator is primarily designed with this function type in mind.

Step 2: Input Function Details

For rational functions, you will need to provide additional information about both the numerator and denominator polynomials:

• Degree of Numerator (p(x)): Enter the degree of the polynomial in the numerator. Valid entries range from 0 to 10.
• Degree of Denominator (q(x)): Enter the degree of the polynomial in the denominator. This value must be between 1 and 10.
• Leading Coefficient of Numerator: Enter the leading coefficient of the numerator polynomial. Any real number is acceptable.
• Leading Coefficient of Denominator: Enter the leading coefficient of the denominator polynomial. Any real number is valid.

Ensure all required fields are filled with appropriate values, as indicated by the input prompts.

Step 3: View Results

Once you have entered the necessary information, the calculator processes the data to provide the following asymptotic details:

• Horizontal Asymptote: This is calculated based on the degrees of the numerator and denominator. The result will be displayed as a horizontal asymptote value or as “DNE” (does not exist) if applicable.
• Oblique Asymptote Present: Indicates whether an oblique asymptote is present, based on the polynomial degrees.
• Oblique Asymptote Slope: Provides the slope of the oblique asymptote if it exists.
• Number of Vertical Asymptotes: Displays the number of vertical asymptotes, which corresponds to the degree of the denominator polynomial.

The results are formatted for clarity, including numbers presented to four decimal places where applicable. Use these outputs to understand the asymptotic behavior of the function.

Conclusion

Your exploration of the asymptotic properties of rational functions is now complete. Use the Asymptote Calculator whenever you need to quickly determine these critical function behaviors.