Math 1050
Final Exam
College Algebra
Fall Semester 2012
Form A
Instructor______________________________Name______________________________________
Student ID____________________________ID Verification__________Section Number _________
Time Limit: 120 minutes
All problems are weighted equally.
No graphing calculators, notes, books, cell phones, or any devices that can connect to the Internet
are allowed.
Scientific calculators with no more than a basic numeric store and recall memory are allowed on the
final exam. Reference formulas that are allowed are attached to the exam.
This exam has three parts
Part I - Ten multiple choice questions - answer all
Part II - Ten open ended questions - answer all
Part III - Ten open ended questions - choose FIVE
_________________________________________________________________________________
INSTRUCTIONS PART I: Questions 1 - 10, Multiple Choice. Answer all TEN questions. Circle the
correct answer. It is not necessary to show work. There will be no partial credit awarded on this part
of the exam.
________________________________________________________________________________
1) Solve the inequality.
x(x + 7)
-12
A) [-3, )
C) (- , -4] or [-3, )
B) (- , -4]
D) [-4, -3]
2) Express as a single logarithm.
2 loga (4x + 1) - 3 loga (4x - 1) + 4logaa
A) loga (4x + 3)
B) loga 4(x + 1)
C) loga (4x + 1) + 4
a4(4x + 1)2
D) loga
(4x - 1)3
3) For the given functions f and g, find the requested composite function value.
f(x) =
x-8
, g(x) = x2 + 6;
x
A) 31
B)
Find (g
f)(-2).
1
2
C) 50
1
D)
1
5
4) Match the correct function to the graph.
A) y = x + 2
C) y = x
B) y = x - 2
D) y = x - 2
5) Solve the equation.
ex - 5 =
A)
1 x+2
e4
7
5
B) -
7
3
C) -
13
3
D) -
6) Find the center (h, k) and radius r of the circle with the given equation.
x2 + y2 + 8x + 6y = -9
A) (h, k) = (3, 4); r = 16
C) (h, k) = (-3, -4); r = 4
B) (h, k) = (-4, -3); r = 4
D) (h, k) = (4, 3); r = 16
2
3
5
7) Compute the product.
1 2
0 -3 1
0 1
5 -1 0
1 -1
A)
B)
10 -5 1
5 -1 0
-5 -2 0
C)
0 10
0 -1
0 0
D)
1 -4
5 9
1 5
-4 9
8) Find the domain of the function.
f(x) =
x
x-3
A) {x|x 0, 3}
B) {x|x 3}
C) {x|x 3}
D) {x|x > 3}
E) {x|x 0}
9) List the potential rational zeros of the polynomial function. Do not find the zeros.
f(x) = -2x3 + 3x2 - 2x + 6
A) ± 1 , ± 3 , ± 1, ± 2, ± 3, ± 6
B) ± 1 , ± 3 , ± 1, ± 2, ± 3
C) ± 1 , ± 1 , ± 1 , ± 1, ± 2
D) ± 1 , ± 1 , ± 1, ± 2, ± 3, ± 6
2
6
2
3
2
2
3
2
2
10) Find the first term, the common difference, and give the recursive formula for the
arithmetic sequence.
10th term is 25; 13th term is 4
A) a1= 88, d = 7, an = an-1 + 7
C) a1 = 95, d = -7, an = an-1 - 7
B) a1 = 88, d = -7, an =an-1 - 7
D) a1 = 95, d = 7, an = an-1 + 7
3
INSTRUCTIONS PART II: Questions 11 - 20. Answer all TEN questions carefully and completely,
showing all appropriate work and clearly indicating your answer.
_________________________________________________________________________________
11) Graph the function. Label at least three points.
x+3
f(x) = -4
-x + 4
if -7 x < 2
if x = 2
if x > 2
12) For the given functions f and g, find the requested function and state its domain.
f(x) = 3x + 4; g(x) = 2x - 5
A) Find
f
(x)
g
B) State the domain of
f
(x)
g
4
13) The function f is one-to-one. Find its inverse. State the domain and range of both the
function and the inverse function.
f(x) =
8
x+8
f-1(x) =
Domain of f(x):
Range of f(x):
Domain of f-1(x):
Range of f-1(x):
14) This matrix is nonsingular. Find the inverse of the matrix. You must show your work for
full credit.
-5 -1
3 0
5
15) Graph the function. Identify the domain, list any intercepts and equations of any vertical,
horizontal, and/or oblique asymptotes.
f(x) =
3x
(x - 2)(x + 5)
Domain:
Equation(s) of Asymptote(s):
Intercepts (give as ordered pairs):
6
16) Given the function f(x) =
2x
+5
x2
A) Find f(-x).
B) Find -f(x).
C) Is f(x) even, odd, or neither? Support your answer using the results from
parts A) and B).
17) Find the present value, that is, the principal needed. Round to the nearest cent.
To get $10,000 after 2 years at 6% compounded monthly
7
18) Find the real solutions of the equation.
x2/3 - 6x1/3 + 8 = 0
19) Solve the problem.
You have 92 feet of fencing to enclose a rectangular plot that borders on a river. If you
do not fence the side along the river, find the length and width of the plot that will
maximize the area.
8
20) Graph the function. Label any intercepts and equations of any asymptotes. State the
domain and the range of the function.
f(x) = log (x - 2)
4
Domain:
Range:
Equation(s) of Asymptote(s):
Intercept(s):
9
INSTRUCTIONS PART III: Questions 21 - 30. Answer FIVE questions only. Show all appropriate
work carefully and completely, clearly indicating your answer. Put an X through the 5 problems you
do not want graded. If you do not cross out any problems, the first 5 problems that show any work will
be the ones that are graded.
________________________________________________________________________________
21) Determine whether the infinite geometric series converges or diverges. If it converges,
find its sum.
100 + 20 + 4 + ...
22) Given that f
2
= 0, find the remaining real zeros of the polynomial function.
3
f(x) = 3x3 - 11x2 - 6x + 8
10
23) Solve the inequality. Express the solution using interval notation.
x + 16
x+3
6
24) Solve the equation.
log2 x + log2(x - 6) = 4
11
25) Solve the problem.
An antenna dish is shaped like a paraboloid of revolution. If the dish is 40 feet wide at its
opening and is 25/3 feet deep at its center, how far from the vertex should the receiver
(focus) be located?
26) Form a polynomial f(x) with real coefficients having the given degree and zeros. Expand
into standard form (do not leave it factored).
Degree: 3; zeros: -3 and 4+ i.
12
27) Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is
not applicable, say so. You must show D, Dx, and Dy to receive full credit.
-2x + 4y = -2
-2x + 3y = -3
28) Solve the problem.
The half-life of radium is 1690 years. If 150 grams are present now, how long (to the
nearest year) till only 100 grams are present?
13
29) Find the center, vertices, and foci of the hyperbola.
x2 - 4y2 + 2x - 24y - 39 = 0
30) Write the partial fraction decomposition of the rational expression.
11x2 + 8x + 8
x(x + 2)(x - 4)
14
The following reference formulas may be used during the Math 1050 final exam.
Students are NOT allowed to use any additional books or notes.
2
2
( x − h) + ( y − k ) = r2
2
2
( x − h) + ( y − k ) = 1
a2
b2
2
2
( x − h) − ( y − k ) = 1
a2
b2
2
( x − h)
2
( y −k)
+
2
=1
b2
a2
2
2
( y − k ) − ( x − h) = 1
a2
b2
2
( y − k ) = 4a ( x − h )
2
( x − h ) = 4a ( y − k )
( y − k ) = −4a ( x − h )
2
( x − h ) = −4 a ( y − k )
A = Pe rt
A = P (1 + nr )
n
S n = ( a1 + an )
2
1− rn
, r ≠ 0,1
Sn = a1
1− r
nt
A(t ) = A 0 e kt
Answer Key
Testname: M1050FA2012 FINAL EXAM FORM A
1)
C
2)
D
3)A
4)
D
D
6) B
5)
7)
C
D
9) A
10) B
11) Three points need to be labeled. Answers may vary. These points do not include (2,5) or (2,2).
8)
y
10
-10
-10
12) [1j(x) =
3x2x-5+ 4;
g
{XIX ¥- ~}
2
13)
f-1(x)
=
-8x + 8
X
Domain of f(x):
x¥-- 8
Range of f(x): y¥-O
Domain of f-1(x): x¥-O
Range of f-1(x): y ¥-- 8
o 1
3
14)
5
-1 -3
15
Answer Key
Testname: M1050FA2012 FINAL EXAM FORM A
15)
y
40
20
-8
-4
4
8
x
-20
-40
Domain: x #;-5, x#;2
Equation(s) of Asymptote(s):
x
= -5, x = 2
Intercepts (give as ordered pairs): (0,0)
-2x
16) A) f(-x)
x2+5
= --
-2x
8) -f(x) =x2+5
C) odd
17) $8871.86
18) {8, 64}
19) 46 feet by 23 feet
16
Answer Key
Testname: M1050FA2012 FINAL EXAM FORM A
20)
y
10
5
-10
-5
5
10
x
-5
-10
Domain:
x> 2
Range: !ll
Equation(s) of Asymptote(s): x
=2
Intercept(s): (3,0)
21) Converges; 125
22)-1,4
23)
(-00.
-3) or [- ;,
00)
24){8}
25)
26)
27)
28)
29)
12 feet directly above the base of the dish.
f(x) = x3 - 5x2 - 7x + 51
x = 3, y = 1; (3, 1)
989 years
center at (-1, -3)
vertices at (-3, -3) and (1, -3)
foci at (-1
-3) and (-1
-3)
-,f5,
30)
..:.! + _3_
x
x+2
+,f5,
+ _9_
x-4
17
Math 1050
Instructor
Student 10
Final Exam
College Algebra
Fall Semester 2012
Form A
-&...
_'__
Name
~.
10 Verification -------- Se~tion Number ----
~
Time Limit: 120 minutes
All problems are weighted equally.
No graphing calculators, notes, books, cell phones, or any devices that can connect to the Internet
are allowed.
Scientific calculators with no more than a basic numeric store and recall memory are allowed on the
final exam. Reference formulas that are allowed are attached to the exam.
This exam has three parts
Part I - Ten multiple choice questions - answer all
Part II - Ten open ended questions - answer all
Part III - Ten open ended questions - choose FIVE
INSTRUCTIONS PART I: Questions 1 - 10, Multiple Choice. Answer all TEN questions. Circle the
correct answer. It is not necessary to show work. There will be no partial credit awarded on this part
of the exam.
1:"2.+7X
1) Solve the inequality.
-+1220
3.lWS.' X -==-~ .muu: I
~
(IX f4){ 'Xf3) 20
x(x + 7) ~ -12
funchon
pCWV
B) (_00, -4]
0) [-4, -3]
MJ-3,00
C) (_00, -4] or [-3, 00)
== -2/ /lUd..C
fll14"44",,,
IUf44f4t.a4
-4
-3
~-~+Q
A) loga (4x + 3)
B) loga 4(x + 1)
C) loga (4x + 1) + 4
3) For the given functions f and g, find the requested composite function value.
§
g(r~2))
g(x)
= x2 + 6;
Find (g
0
f)(-2).
B)~
2
O)~
C) 50
~
5
1
"2..
5 +0
25 +.6 ::: -3)
-=
2-
@
(f;
2) Express as a single logarithm.
X
/
4) Match the correct function to the graph.
y
pafml-
Pun{jir,
r;
hOfljdYl-M-J 'Shih Ojhf- 2 UJ1Iff
-5
x
5
-5
A) Y
= ~x + 2
8) Y
5) Solve the equation.
e'-5=[~r
=x-2
-'i) X+1-
e : e
)(-5
-'=r
(.
=
X-5 ~ - 4(Xf2)
6) Find the center (h, k) and radius r of the circle with the given equation.
X2 + y2 + 8x + 6y = -9
(/f..l + Z I)( +Iit; ) + (y ~t: 0'j-t-Cj ) :::. -1+1{;+7
(1X+4j2. t 1- 3 z..:::. Ih z: 4
7.-
=
=
A) (h, k) (3,4); r 16
C) (h, k) = (-3, -4); r = 4
8 (h, k)
2
= (-4, -3); r = 4
(O)(z)
(0)(1) -== 0
7) Compute the product.
e-3)(O)
= I_
U )(1)
0 -3 1] 1 2
t:3)( I )
-:::0
(;)(-1)
::: -
3
= -/
-4
I
[5 -1 0 0 1
1 -1
~x2.
t.X3
A~
/'
8)
D)
o
o
o
10 -5 1
5 -1 0
-5 -2 0
10
[~4~]
-1
0
(:;)(1):; 5
t:-J )((»)
8) Find the domain of the function.
f(x)
=- 0
=
-::/:.O(
/X. - 3
x
~
z: D
(5){2)
==-/0
f: J )(,)
-::::
J
-
(Qj{-J) :::
(P){/) ~
~-37{)J-'1X--3)D
-
5
0
/X.73
t
9) List the potential rational zeros of the polynomial function. Do not find the zeros.
Ix
1
A)
± -,
2
!'/i. 'J-", -r(/A~~~
aultx5
~H : +(
"-c.-rzr.rS 0 -2.
1
3
=-~+6
3
± -,
2
± I, ± 2, ± 3, ± 6
3/1e
I
8)
± -,
D)
±.:!.., ±.!., ± I, ± 2, ± 3, ± 6
2
3
± -,.±
2
I, ± 2, ± 3
.
2
10) Find the first term, the common difference, and give the recursive formula for the
() 11 ::::
arithmetic sequence.
10th term is 25; 13th term is 4
A) a1= 88, d = 7, an = an_1+ 7
C) a1 = 95 , d = -7 'n a = a n- 1 - 7
Z 5 -:::
Cl +d (Jo-!)
~6 -:U f 'td
j
j
4 ~ a) fd (/3-1)
4 -:;:.
tI,
f-12
- 25 ::::-lA,
d
-Cjd
QJ
-f
dt
a
-j
z: 01n-t
- 1-
~)
INSTRUCTIONS PART II: Questions 11 - 20. Answer all TEN questions carefully and completely,
showing all appropriate work and clearly indicating your answer.
11) Graph the function. Label at least three points.
f(x)
=
if x 2
if x > 2
l-x +4
M a( k off.: : : : : : : .
() pOln:Y ltJd1:
If -I1u ~tlt;
: . . . ..
~.
5
.
Y
.
•
•
.
•
..::::
.
foy ~::: X+3
· ~r~ph 0 -== ~
.
..
-+-+..-+-+-+-+-*-+--t-+-.~.
.
.
C-11-4> : :
x
.
.....•
.-5
LJ
, cJose.d c" rc lL- a t ~-::
-L.J
• grttph ~ ~ -X-t~
• prD Pu ..tfltt pOln B for
8 --=- -x t.LJ
: : : -:
1.. tj) D y(t 2-f-+) -+-+7.-+-( 1
1 ...
0::: x+ 3
• prDpt( .t¥ld pOIr1if
:5/
. ..
pDJnts I ndudt;:
_.
I p+ each
· 9rdfh
if -7::;; x < 2
x +3
= J -4
(1-(~}•...
lprs
.f1N ItlbeJJn~ atkil5 + 3 torre.Lr- pD)nfs
co In 11 MAl! va (\J .
12) For the given functions f and g, find the requested function and state its domain.
f(x)
= 3x + 4;
A) Find [ ~ (x)
J
g(x)
= 2-x?5
f(x\
g60
-
3X+4
2x -5
B) State the domain of [~]<x)
2X-'S -:f0
1)< ::fr 5
X
4
=F
%
I
13) The function f is one-to-one. Find its inverse. State the domain and range of both the
function and the inverse function.
I \plr-0 -:::
f(x) =_8_
x+8
f-1(x)
=
- ?3X+'6X
=
X
X -f:-8
Domain of f(x):
!j f
Range of f(x):
0
Domain off-1(x):
)(-=/::O
Range of f-1(x):
!j t -g
14) This matrix is nonsingular. Find the inverse of the matrix. You must show your work for
full credit.
101-
[-~-~l /
[-~
r
-~ I ~ ~]
/ I 3-
_3
I
0]
5"
[
3rJ + 5~
"3 r, + (2-
.,.
-;
I~
--;
[/?
0
5
0
-3
f
0J
-Ir,
r
6
J{5n
0 ~]
3
-I/~ (z
I~
15) Graph the function. Identify the domain, list any intercepts and equations of any vertical,
horizontal, and/or oblique asymptotes.
f(x) -
(X-Z)(X+5)
3x
(x - 2)(x + 5)
Domain:
X i= 2/ x;f -5
Equation(s) of Asymptote(s):
X =j:. 2.
2P+ s
X:::: '2/
X
z:
-5;
Ipt--
Intercepts (give as ordered pairs):
6
~O
X
0 ~0
f. -5
3pfs
X--:::.D:
F /o) ::: D
16) Given the function f(x) = 22X
x +5
+(-X)
A) Find f(-x).
8)
Find -f(x).
-
r (X)
2 (-x)
t: X) 2.1-5
-
-:::. - ( 2
3p+-s
X) -
X .z.+6
C) Is f(x) even, odd, or neither? Support your answer using the results from
parts A) and 8).
f(x) k; Ddd.
f
f-x)
==--{{x)
2pts
17) Find the present value, that is, the principal needed. Round to the nearest cent.
To get $10,000 after 2 years at 6% compounded monthly
A
A
-::.p{J-+fJ)n-l:
P==A(I
2p+s
-:::..tJ DODD
t: ::: 2 ~~(5
r -:::.
/:;10 -:::: 0 h
I
n
p::::
7
. r) -nt
+---..
n
correc.tfor~
18) Find the real solutions of the equation.
~
u
-=-
~:
U -w + g
2-
(u - 4)(U-2)
U-=- 4
«»
z: D
:::0
3 -:: 4:3
'X ~ 64
u::2-
un9Ab'ih'hdL .'
1'/3:::
\'S
1-- r
4
1 piIX.
IB z: 2
19) Solve the problem.
You have 92 feet of fencing to enclose a rectangular plot that borders on a river. If you
do not fence the side along the river, find the length and width of the plot that will
maximize the area.
KJue-r
A ~ xlj
A:::
A (x)
x{q;)'-:Jx)
-=::
-
2 X z. -t q ~)(
lj
Z- pt- S
2x+fj
z:
~ z:
\?~
q;L
9:L -2:x
- qJ- d (-~) -- ~3
~p\-S
h~ -0
;;<C1
0-:::
rx
X
q~- ~(~~
40
!j::: 40
8
fj
b'j 2S!-+-
\'P\-
20) Graph the function. Label any intercepts and equations of any asymptotes.
domain and the range of the function.
f(x)
=
X-2 '/
log (x - 2)
X
4
Domain:
\pt-
X '/;6
0
'2..,
\ P 1-
Range:
X:::
Equation(s) of Asymptote(s):
Intercept( s):
>
State the
(3/D)
·8
. ("
4
• ,.
2
•
. -8 . -6 . -4 . -2 ~2
•
.-4
•
-6
----'2. p+-S
v 1-
6
r
~
'1W !JHnJerupf-
,}J-==-O.'
0 -z IOS/X-2)
4° -::::X -2.
I -= X-2
3 -:::
X
r
r•
Ip+-
-;;L
4
• 6
.
8
.
lie
3pi-s
9
(3/0)
.
INSTRUCTIONS PART III: Questions 21 - 30. Answer FIVE questions only. Show all appropriate
work carefully and completely, clearly indicating your answer. Put an X through the 5 problems you
do not want graded. If you do not cross out any problems, the first 5 problems that show any work will
be the ones that are graded.
21) Determine whether the infinite geometric series converges or diverges. If it converges,
find its sum.
OJ
100 + 20 + 4 + ...
r
z:
/00
-=
/ r/
20
J
j{){)
5
1-p\-S
tErJU.vl~
~I
.
/00 (
/00(5)
f(x)
= 3x3 ~
= 0,
11X2
-
find the remaining real zeros of the polynomial function.
6x + 8
-~
-11
"3
3
3X2-
-0
-<g
-Cf
-/2-
0
-/2
3X
- L/)
?J ( x 2-
-
3(X
-4)(X+J)
X-=-
<g
2-
qX
if
::: 0
=
0
D
X
-::2- )
10
7)
4f*5
4
22) Given that f[;]
I
3pts
23) Solve the inequality.
Express the solution using interval notation.
CYlhLiJ
x + 16 s 6
x+3
IX. -/-Ift, -b
vttiutJ:
X::::-3
I p+-
0
L
1( ::. -0/ 5
Xt-3
j
L. 0
I r+
rg -< 0
2p+s
Hh - b(X+3)
X+3
X+3
IX +10 - fo~ -J
/)(+3
-5x - ~ ~ 0
\ pt-
~+3
24) Solve the equation.
log2 x + log2(x - 6)
~
v2-
.2 4
=4
[X (X-h)
_
x ( 1( - (,)
1ft; ::: 'X
o -::: 'X
0-=
]
2.
L-
6'1'
=4
2p+s
2 p1- 5
lp\:S
\ pr
-6y. -/0
(X-<J)(X+2)
-1:=g
\pr
IJ)(Z
JJXfmr;~
\pt DH
11
s:
I~
"
0.5 ().(\~
25) Solve the problem.
An antenna dish is shaped like a paraboloid of revolution. If the dish is 40 feet wide at its
opening and is 25/3 feet deep at its center, how far from the vertex should the receiver
(focus) be located?
)
•.....--' f>t-
40
c
- - -J
/
__
~~/
12o,
'2-5L
~
(2.
/3 ,
SOIU;\-IDvl
__
\ \01
-= 4 a (lj- k)
(1.0 -0) -=- Lla. ( -0)
'X-h)
pi-
2;
2-
11 f-t- d\ye'eJ Iy
(AboUL
bM0
Ot ~
~~s
26) Form a polynomial f(x) with real coefficients having the given degree and zeros.
into standard form (do not leave it factored).
Expand
Degree: 3; zeros: -3 and 4+ i.
X ::::4 -.A.-;?( -
;;<-+3 ~D
4
-.,;l; :::
'X-4-1-L
D
::..D
-f{x) ::::( ~ +3) (-X -4 -/I.) ( ~ -4 -I-.i)
f (X) -:: (Xt3) (Xl.
f (x)
"X
3 -
:::- 'X 3>
-
-(-0
-ff{ - il)
0 -4x + lb - f, -~
- (')(-t-3) (~2 -1)X + Fr)
+' (~) -
t (x)
-41}:' +
+J
~X2.
+ Jil< +
S X~
- 7X
+
1- p\-S
3'X~ - 24')< t '5
6}
J
2p-l-S
27) Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is
not applicable, say so. You must show 0, Ox' and 0y to receive full credit.
f-2x + 4y =-2
l-2x + 3y = -3 '
-2
-2
Dx::
I :::~ ;) -
-'2-1 -::: (-2)(-~)
-2..
D~ :::- 1
2
-= - ro +
(-2-) ( :,) - ( -3 ) ( 4)
- (-2)(-2)
:=
en -
I2
'1 -
2-
-3
X -
Dx --
-P
tJ~ ~::
.Ia: - 3
:L-
% ~}
28) Solve the problem.
The half-life of radium is 1690 years. If 150 grams are present now, how long (to the
nearest year) till only 100 grams are present?
<.
~F*/ A ~
ve
rt
P =
r (It~qo)
\£30
J- -
e
150
A -::: 75
(:-4. ID I .tt " 2b G -~)
70 ~ ISD~
\ SO
t:::' bCf D
hO\ I t I \ C6:
10Qvr
C-
lOD ~ 150 c.
150
"2-
~ (t) :::
l~i1Dr
2-
lSQ
(
)
3~b
J;n( ~) ~ (
~~r
)l
I lot} 0
~l ~)
r ~ - 4. IDl4 020 f-L}
::: t.
- 4. I0 l4 G2ft> e-~
13
t ~ 91)<3, S'3~02b2.
1:; ~ a, 1>q
(V1;Y
\
f
a -::::2-
29) Find the center, vertices, and foci of the hyperbola.
X2 -
4y2 + 2x - 24y - 39
b:::/
=0
- 3Cf
--4~2.-~A~
) - -4 (y2. + rot:)
) -:::
34
( 'X 2+ 1x + I) - 4 (~2-. f- b0 -t q )
('XfJ)2- -
-
4(0+3)2-
~
(I)(
\ft
~
+ I)~
2 z,
. ~
-
~
_ ( ~+ 3) 2.::::
I 2--
\
(-1 ttf3}-~)
30) Write the partial fraction decomposition of the rational expression.
11X2 + 8x + 8
x(x + 2)(x - 4)
l\)(2.+<6x
+~::
-::::
A
X
+~
B
X +2
x- c::g '3p1- s
(-J-V3j--3 )
A (X+2)(X-4) t B(x)(x.:-4) tC(X)(X+2)
W )(-=- 0: Q--_oA
0
+
0
A===-\
2-llo -=- lLi G
14
~
_
'3p+.5
I t+