## Tutoring on Determining Equations of Rational Functions

Learning Objectives:

#### Understand to Determine Equations of Rational Functions.

Math Tutoring on Determining Equations of Rational Functions

A function of the form where f(x) = a(x) /b(x) are polynomials is called a Rational Function. The graphs of rational functions can be recognized by the fact that they break into two or more parts. These parts go out of the coordinate system along with an imaginary straight line called an Asymptote. Vertical asymptotes can be found by solving the equation b(x) = 0 where b(x) is the denominator of the function f(x).  This only applies if the numerator a(x) is not zero for the same x value. Horizontal asymptotes can be found by finding the limit of f(x), x→∞. A rational function in which the degree of the denominator is higher than the degree of the numerator has the x axis as a Horizontal asymptote. If the degree of the denominator b(x) is the same as that of the numerator a(x) then we find the asymptote by calculating the limit of f(x), x→∞. If the degree of the denominator b(x) is one less than that of the numerator a(x) then we can find the equation of the Slanting asymptote by division.

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Hook Questions:

1.    How do you graph a function?

2.    What is the definition of a rational function?

3.    How do you find Asymptotes?

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