Rational Functions

Site:	REMC 8 / Kent ISD Moodle VLE
Course:	Algebra II - Staublin
Book:	Rational Functions

Printed by:	Guest user
Date:	Tuesday, May 14, 2024, 4:50 PM

Description

Learning Objective

Describe graphically, algebraically, and verbally real-world phenomena as functions; identify the independent and dependent variables.
Use rational functions to solve problems. Solve by graphing, factoring, finding zeros and asymptotes through analysis of the polynomials in the numerator and denominator, and use properties of equality.

There are five assignments: review each assignment with your teacher before proceeding to the next.

1- Vertical Asymptotes and Roots

Explore Vertical Asymptotes and Roots with your Graphing Calculator - click the link to jump to the activity.

What is a rational function?

What is a discontinuity?

Help for Vertical Asymptotes and Roots

More Vertical Asymptote info

Purple math has a nice summary of Vertical Asymptotes here.

Function Grapher

The web-site "Math is Fun" has a pretty good function grapher, if you ever need one.

ANSWER KEY - Vertical Asymptototes and Roots

Click the link for the Vertical Asymptotes and Roots ANSWER KEY.

2- Removable Discontinuities

Explore removable discontinuities with your graphing calculator - click the link to jump to the activity.

Factoring Reminder

The quick-check at the top of Activity #2 requires you to factor a quadratic trinomial with a lead coefficient not equal to the number one. Remember how? Here's a reminder:

Vocabulary

Roots, Infinite Discontinuities, Removable Discontinuities

What are they?
How do they occur?

Removable Discontinuities

What's a removable discontinuity and what causes them?

ANSWER KEY - Removable Discontinuities

Click the link for the Removable Discontinuities ANSWER KEY.

3- Horizontal Asymptotes

Explore Horizontal Asymptotes with your graphing calculator - click the link to jump to the activity.

Limits and Horizontal Asymptototes

Here's a quick lesson on how limits work. More info below the video.

Wikipedia has a pretty good article on limits.

Limit Notation from Oregon State University.

More Horizontal Asymptote info

Purple math has a nice summary of Horizontal Asymptotes here.

ANSWER KEY - Horizontal Asymptotes

Click the link for the Horizontal Asymptotes ANSWER KEY.

4- Oblique Asymptotes

Explore Oblique Asymptotes with your graphing calculator - click the link to jump to the activity.

Long Division review

Here's a little review of long division, then some help with the first two explorations in the Oblique Functions packet.

Example, finding an Oblique Asymptote

More Oblique Asymptotes info

Purple Math has a really good example and summary of Oblique Asymptotes here with a really good explanation of how horizontal and slant asymptote rules pretty much reduce to the same thing: divide, and ignore the fractional part.

ANSWER KEY - Oblique Asymptotes

Click the link for the Oblique Asymptotes ANSWER KEY.

5- Applications

Use your knowledge of rational functions to solve real-world problems - click the link to jump to the problems and solve "You're Toast, Dude!". We'll tackle the other problems together in class.

ANSWER KEY - "You're Toast, Dude!"

Click the link for the "You're Toast Dude!" ANSWER KEY.

6 - Asymptote Summary, Examples and REVIEW

Click the link for my summary with examples.

Click this link for the Rational Functions REVIEW packet and the Rational Functions REVIEW packet ANSWER KEY.

Click this link for a basic summary of asymptotes from mathisfun.com, and I highly recommend checking out these asymptote examples from purplemath.com.

7 - Adding/Subtracting Rational Functions

Assignment

Textbook 9-5: 1-3, 10, 11-21 odds, 31-39 odds, 52-55

Resources

9-5 Answer Key

8 - Solving Rational Function Equations

more to follow

9 - More Applications

This worksheet, 9-6 Problem Solving Worksheet, has story problems (and answers).

These worksheets, 9-5 & 9-6 Review Problems Worksheet and MORE 9-5 & 9-6 Review Problems Worksheet, cover story problems, adding/subtracting rational expressions, and solving rational function equations (with answers).