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
TRANSCRIPT
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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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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
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Chapter 9 Review
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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
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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 :
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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
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1:
Range
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writecanyouor5
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NumbersRealAll:Range
,22,
writecanyouor
2except
NumbersRealAll:Domain5
2:
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yHA
xVA
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Graphs of Rational Functions – Check HW
nm
nn
mm
x
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m
n
m
011
1-nn
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b
ayat
asymptote oblique hasIt HA. no n,m If
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:sticscharacteri following thehas
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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
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12
42
2
xx
xy
xx
xy
9
233
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x
x
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2
2 7
7
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x
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7
)7(
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)2(4 xx2
)2(2 x)4)(2( xx
86
42
2
842
xx
x
x
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)4(
)2(4
xx
x
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42
2
65
4
9
3422
2
2
2
x
x
xx
x
x
xx
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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
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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
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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
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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
)(
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2
54
2
102
xxxx
33
11
2
xx
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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_____________________
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• 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
•