Oblique Asymptotes

An Oblique Asymptote occurs when the degree of the numerator is greater than the degree of the denominator. To solve you need to use long division. You divide the numerator by the denominator.

Step 1: Divide the numerator by the denominator using long or synthetic division.

Step 2: Only find the terms that make up the equation of a line. (No remainder)

Step 3: Graph

Oblique Asymptote: y=x-2

**Graphing:**Let's say that the vertical asymptote of a function was -2. First, plot the vertical asymptote.

Next, plot the line we found for the oblique asymptote.

**"Proper" Functions:**

\begin{equation} x^2+2x+0 \end{equation}

If the degree of the numerator is less than the degree of the denominator then the equation is "proper" which means that y=0.

**Example:**

\begin{align} f(x)\frac{5x-2}{3x^2+3x-1} \end{align}

x is less than x^2 so it is proper.