Lesson 2.4: Properties of Rational Functions

Lesson Overview:

How to find the following properties of rational functions---

Dahry: Domain, Vertical Asymptote , Horizontal Asymptote, Oblique Asymptote, Hole Roots, and y-intercept.

Dahry Diagram

Real World Example

What is the average price of movie tickets, where the first is $12, and each additional is $9, as more and more tickets are purchased?

This question can be solved with: P(t)=(9t+12)/t, where P(t)is price per ticket based on number purchased, and t is the number of tickets.

Solving using the Dahry diagram, we see a horizontal asymptote at 9, representing the price that each ticket approaches as more and more people (or tickets) share the additional cost of the first ticket. Note that if you were actually buying ∞ tickets, the price per ticket would mathematically be $9 per ticket!

SAT Practice