Lesson 10 Horizontal Asymptotes of Rational Functions

Lesson 10 Horizontal Asymptotes of Rational Functions

Presentation

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF-IF.C.7D

Standards-aligned

Created by

Anastasia Avila

Used 51+ times

FREE Resource

5 Slides • 10 Questions

1

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

Lesson 10 Horizontal Asymptotes of Rational Functions

2

Dropdown

Question image

Real zeros of n(x):

Real zeros of d(x):

Hole(s):

V.A.:

Domain:

3

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

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)

4

What is N or D refer to?

How to FIND the horizontal asymptote

5

Together:

6

Try these on your own

7

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

Type answer...

8

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

Type answer...

9

Multiple Choice

Question image

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

1

No

2

Yes, y=0

3

yes, y=3

4

yes, y=1/3

10

Multiple Choice

Question image

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

1

No

2

Yes, y=0

3

yes, y=3

4

yes, y=1/3

11

Multiple Choice

Question image

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

1

No

2

Yes, y=0

3

yes, y=-5

4

yes, y=1/5

12

Multiple Choice

Question image

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

1

No

2

Yes, y=0

3

yes, y=-5

4

yes, y=1/5

13

Multiple Choice

Question image

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

1

No

2

Yes, y=0

3

yes, y=2/3

4

yes, y=3

14

Multiple Choice

Question image

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

1

No

2

Yes, y=0

3

yes, y=1

4

yes, y=2

15

Open Ended

Question image

Type your summary below.

Type response here

pattern-tertiary

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

Lesson 10 Horizontal Asymptotes of Rational Functions

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