m—06/07/10—hw #75: pg 550: 11-19 odd; pg 558: 29-49 eoo; pg 566: 27-39 eoo; pg 572: 43-49 odd

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M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

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Page 1: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

Page 2: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

T—06/08/10—HW #76: Pg 550: 20-22; Pg 558: 31-47 eoo; Pg 566: 29-37 eoo; Pg 572: 42-50 even

20) A 22) B

42) -1, 6 44) -2, 5 46) 1, 6

48) -6 50) -4

Page 3: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

Chapter 9 Review

Page 4: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

linear.areand,sectionthisFor.0)(and

spolynomialare)(and)(where,)(

)()(

formtheofisfunctionrationalA

qpxq

xqxpxq

xpxf

branched a called aregraph theof parts thewhere

HYPERBOLA,aisgraphoftypeThis

The vertical asymptote is x = h, h is where the denominator equals 0.

32

3

x

y82

53

x

xy

2x 4x

Page 5: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

khx

ay

dcx

baxy

42

3:

x

yEx

4: yHA

42

3:

x

xyEx

2

3: yHA

Domain: all real numbers except ‘vertical asymptote’

Range: all real numbers except ‘horizontal asymptote’

There are two types of graphs you will deal with in this lesson.

kyHA :c

ayHA :

Page 6: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

Look at problems you did and fill in Vertical asymptote, Horizontal Asymptote, Domain, Range

21

3

x

y105

32

x

xy

),2()2,(

writecanyouor

2except

NumbersRealAll:

),1()1,(

writecanyouor

1except

NumbersRealAll:Domain

2:

1:

Range

yHA

xVA

,5

2

5

2,

writecanyouor5

2except

NumbersRealAll:Range

,22,

writecanyouor

2except

NumbersRealAll:Domain5

2:

2:

yHA

xVA

Page 7: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

Graphs of Rational Functions – Check HW

nm

nn

mm

x

xxx

xxx

n

m

n

m

011

1-nn

011

1-mm

b

ayat

asymptote oblique hasIt HA. no n,m If

b

ay :HA then n, m If

0y :HA then n, m If

HA onemost at has f ofgraph The **3.

q(x) of zeros realat VA hasGraph 2.

p(x) of zeroes real theare f of intercepts- x1.

:sticscharacteri following thehas

aa...aa

aa...aaf(x)

function rational theofgraph The 1.than

other factorscommon no with spolynomial be q(x) and p(x)Let

POWER

Bottom degree bigger

Same

Top degree bigger

Page 8: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

12

42

2

xx

xy

xx

xy

9

233

Page 9: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

xx

x

x

xx

2

2 7

7

78

42

86

2

84 2

x

xx

x

x

)7)(1( xx

)7( xx7

)1( xx

)1(

7

)7(

)7)(1(

xx

x

x

xx

71

7

)2(4 xx2

)2(2 x)4)(2( xx

86

42

2

842

xx

x

x

x

)4(

)2(4

xx

x

Page 10: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

42

2

65

4

9

3422

2

2

2

x

x

xx

x

x

xx

Page 11: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

22

53

x

x

x

x

3

4

3

4 25

x

x

x

x

1

1

1 22

xx

x

1

2

1

3

x

x

x

x

2

8

x

x

x

8

3

43

x

x

x3

)1)(1(

1

xx

x

)1(

1

x

1

22

x

x

21

)1(2

x

x

Page 12: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

1

4

1

12

xx 4

1

2

2

x

x

x

x

1

4

)1)(1(

1

xxx

)1(

)1(

1

4

)1)(1(

1

x

x

xxx

)1)(1(

44

)1)(1(

1

xx

x

xx

)1)(1(

54

xx

x

)2(

)2(

)4(

)1(

)2(

2

)4(

)4(

x

x

x

x

x

x

x

x

)2)(4(

)2(

)2)(4(

82 22

xx

xx

xx

xx

)2)(4(

292

xx

xx

)2)(4(

282 22

xx

xxxx

Page 13: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

7

24x x

15

5

3

1

2

2

1610

)2(22

xxx

x

3

1

4 x

x

x228

x14

x1515

x0

432 xx

0432 xx

0)1)(4( xx

1,4 xx

3220282 22 xxx

x2040

2x

DOUBLE CHECK!Plug in to see if it works

Page 14: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

1

1

12

xx

x

DOUBLE CHECK!

)1)(1( xx

)1()1()1)(1(2 xxxxx

1

1)1)(1(

1)1)(1(2)1)(1(

x

xxx

xxxxx

)1()()22( 22 xxxx

122 xxx

032 x

32 x

3x

)(

Page 15: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

2

54

2

102

xxxx

33

11

2

xx

Page 16: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

Find the x-intercepts and vertical asymptotes of the graph of the function

16

5922

2

x

xxy

)12(76

22 23

2

xx

xx

x

Simplify

4

86

2

1682

22

x

xx

x

xx

Simplify

4

6

82

152

xxx

x

Simplify

44

2 2

x

x

x

x

Solve

Name_____________________

Page 17: M—06/07/10—HW #75: Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd

• M—06/07/10—HW #75: Pg 543: 11 – 19 odd (asymptote only); Pg 550: 11-19 odd; Pg 558: 29-49 eoo; Pg 566: 27-39 eoo; Pg 572: 43-49 odd; Pg 580 3, 5;

• T—06/08/10—HW #76: Pg 550: 20-22; Pg 558: 31-47 eoo; Pg 566: 29-37 eoo; Pg 572: 42-50 even

•