Lesson 10 Horizontal Asymptotes of Rational Functions

We will analyze rational functions to determine its horizontal asymptote algebraically.

I will summarize how to find the horizontal asymptote, if any, of rational functions algebraically.

TEKS 2A.6K

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Lesson 10 Horizontal Asymptotes of Rational Functions

Dropdown

Real zeros of n(x): ​

Select answer

Real zeros of d(x): ​

Select answer

Hole(s):​

Select answer

V.A.: ​

Select answer

Domain: ​

Select answer

​Rational functions are in the form of one polynomial over another polynomial.

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Remember...

Types of discontinuities - these break up the graph

• Holes (new) - affect domain (x's what goes IN)

• Vertical asymptotes- affect domain (x's a.k.a. what goes IN)

• Horizontal asymptotes (today) - affect the range (y's a.k.a. what comes out)

What is N or D refer to?

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How to FIND the horizontal asymptote

Together:

Try these on your own

Fill in the Blanks

Does example 3 have a horizontal asymptote? Enter YES or NO,

If YES then enter the asymptote like this below:

(how to input): YES,y=0

Fill in the Blanks

Does example 4 have a horizontal asymptote? Enter YES or NO, if YES then enter the asymptote like this below:

(how to input): YES,y=0

Multiple Choice

Does this rational have a horizontal asymptote? If so what is it?

• No

• Yes, y=0

• yes, y=3

• yes, y=1/3

Multiple Choice

Does this rational have a horizontal asymptote? If so what is it?

• No

• Yes, y=0

• yes, y=3

• yes, y=1/3

Multiple Choice

Does this rational have a horizontal asymptote? If so what is it?

• No

• Yes, y=0

• yes, y=-5

• yes, y=1/5

Multiple Choice

Does this rational have a horizontal asymptote? If so what is it?

• No

• Yes, y=0

• yes, y=-5

• yes, y=1/5

Multiple Choice

Does this rational have a horizontal asymptote? If so what is it?

• No

• Yes, y=0

• yes, y=2/3

• yes, y=3

Multiple Choice

Does this rational have a horizontal asymptote? If so what is it?

• No

• Yes, y=0

• yes, y=1

• yes, y=2

Open Ended

Type your summary below.