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Created page with " Prior Lesson | Next Lesson ==Objectives:== * Identify rational functions and find possible ho..."

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[[8.2: Short-Run Behavior | Prior Lesson]] | [[8.4: Short-Run Behavior of Rational Functions | Next Lesson]]
==Objectives:==
* Identify rational functions and find possible horizontal asymptotes
* Give long-run behavior of rational functions (find a power function that describes the behavior for large values of $x$)

==Important Items==
===Definitions:===
rational function

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==Lesson Guide==

===Warm-Up===
Have students do Problem 1.

===Identify rational functions and find possible horizontal asymptotes===

A [[rational function]] $r(x)$ is a function that can be written in the form $r(x)=\frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomials and $q(x)\not=0$.

Have students do Problems 2 and 3.

Use Problem 3 to discuss what the long-run behavior tells us about horizontal asymptotes. Refer back to the definition of a horizontal asymptote from \S4.4.

===Give long-run behavior of rational functions (find a power function that describes the behavior for large values of $x$)===

Give examples of rational functions that illustrate different types of long-run behavior (i.e., $\pm nfty$ vs. horizontal asymptote).

* Example:
 
 
 
 
 
 
* Example:
 
 
 
 
 

Have students do Problems 4 and 5.

You may need to review limit notation for Problem 5.

Discuss Problem 6 as a whole class if time permits.

==Comments==
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8.3: Long-Run Behavior of Rational Functions - Revision history

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