Learning Objectives:

__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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