Review 9.7-10.5& Application Problems
Due Wednesday,fanuary 30tt'
Failureto show all work will result in a LaSalle.
1JIf f(x) = x' -x, andg[x) = Ji, th.n f[f(4))= ?
1 i ' t "i\ ' : :i ;
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l
lf 'ggzl,i=
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l
(.,'i '' Li
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3 ) If f(x) = 4 - xand g(x) = 6x +l l, theng(f (0))=t
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2) If f(x) = x+ 4 andg(xJ= 3x - 2 then
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Honnrs Geometrv
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4) lf (f " gXr) = J*\ 1,what arethe possible
valueof f (x) and g(x) ?
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r 'i'ii(
i('rdir
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:: t
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A. f ( x) =1fi.r 1 i g( x)= x2
B. f
(*)=Ji ; g(r)- t ;i-
C.f ( i = J r - l
; s @ ) = x z+ 2
D All of the above are valid.
E.A and B only
s)
HEXAGONS A box of chocolates shaped
like a regular hexagon is placed snugly
inside of a rectangular box as shown in
the figure.
6) WIN DOWS A large stainedglass
window is constructedfrom six 30"-60"
90o triangles as shor,vnin the {igure"
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30o,rl
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What is the height of the windor,v?
If the side length of the hexagon is 3
inches, what are the dimensions of the
rectangular box?
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7)
isa
isapark
inyour
town
that
Ptoblem
$olvin$
There
Extended
plan
from
one
corner
of800
feet.
You
towalk
with
aside
lengh
square
totheopposite
corner
ofthesquare
'L
I,
,t
isthedistance
from
foot,
how
much
shortel
Tothenearest
a,Compare
thediagonal
than
the
corner
along
corner
totheopposite
one
',
,
sides
ofthe
square?
distance
along
two
,1,u , ,j ,,,,,,,, I
your
per
pethour,
rate
Find
infeet
atarate
of3miles
b,lbuwalk
second,
.
1i,
. .I
!t
)
r
'.
ii
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:
'Jni'
t ,t to',,". , Jl;;, t
,",,'
,,'t
t
you
would
save
by
how
much
time
Tothenearest
second,
c,Interpret
of
walking
along
fwosides
than
walking
along
thediagonalrather
Lt"'::
t'
t h 0 s' q u a r e ? i t
I
tttl
,v\.
,
t'/.'!
i/'i
rrr
j
I
r
,
,"i
i.
I ,r, l,:.,
1 m i = 5 2 8 0f t .
to tighten
a ttut,Eaclt
therightsizet'rrrenclt
Wrenches
Younurstchoose
o,r.-.,
cltoose
at,r,rettch
size
ofj inch.Youshoulcl
eclge
ofthenuthasa length
tlrt
li'l i
'l ,'' /
i
tothe
,rros tltettutfrontoneeclge
totheclistartc*
tliatisclose
i
t , ''l)
/
youuse, inch, inch,or
sizeshoulcl
Whiclttvrench
opposite
eclge.
f
fr
I.
lllcl)f
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t -,
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9J
' Given , .t!
=r, what value(s)of x will make
x'+l2x+36
the expressionundefined?
10) Theexpression1]
J;
is undefinedwhen x is:
,/.. <. ( '
\'rit(
/
rt
)'(
'L
r \.( (/.
Ll
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11) If x is a real number,andthe value _ r_
eg
15
x+)
undefined,what is the valueof x + g?
X = -5
X r b 'O
12) ltVhatis the.pro
the following.*pi.rrio n undefindd?
4
7+gz +t4
& +z)G+a)
-5 r'X tA
=Q
7="'7''7
??LD -lq
13) lf g[x) = 31
f . g(x).
14)Compute(g fX-) uringthuf*Eon,
"
f ( * ) = x 2 + l a n d g ( x )= 2 x - 5
F (2"-r) ' (3 x-t)' * t
J(x'+r) = z(x'+t)- 5
I*z-(,,^
1 5 ) l n a 3 o o - 6 0 o - 9 0 "t @
largeris the l"fge. legthanthe shorterleg?
qla
Qctrgzn /tX .to F ar.ap
.Q.a,t4tn tA.atv
fA-/
.Azn.tzz
16) Findthelengthorr@
trianglebelow.
"\ = tz {fn
4 Et . l t , q " o a
17)Findx andy.
tl
W' L{
-r
\l
!a
I
.*AI
E*IF
r'-
| tv'3
x\
^,
1l!: b{7
JI .y=A
=y =2t,;')1A
}u1,g
-
tf
}.I
18)In a 45"-45"-90o
triangle,ttre
hypotenuseis /Z timesaslongaseach
leg.
20) Thepjnqreterof an equilateraltriangleis 36 inches.
Roundto the nearest
Findthe@realof
the equilateral.
19) If two anglesof onetriangleare congruentto two
.
anglesof anothertriangle,then the trianglesare -
tenth'
Sirn-i lctr
3:-= ?: -m
3
l\
>./:\s
4 nNtu A,W '5i*, /<a^'{-y
,/
3
l{t \
+" !! =sLG '6G
/-j--L*'
r*'
$
'jL = b
A.4riu=U1)!,v)(')
1\'/")frz)U't7)
X (o2.''l inrhiu.z
For problems #2L-26, use the table definitions of H(t) and r(t) shown below to ffnd the indicated value.
27) (r o tI)(2.s)
22)(r o fl(1.0)
23)(H o r)(2.2)
24)(Ho r]gg)
r(';-tr;l
,t=6=V;3
((a,o)'z,a
t4(z,D')=@
26)(r orl!?{)
=61
((7,o)
t-i(2,il=m
oJcarsMp.r d4y)pro}ucedata
28) THenury{ber
hasa new productto sell.
27) Atoy manufacturer
tactoTy
an{ thoy6 ot g{eratiy(issiy{nav ry6 -/
Thenumberof unitsto be sold,x, is a functionof
LW - syl,wn{et vylesrry{noty{o. rctfcoT{ c 1in
the price,p in the equationx(p)I 3p - 25p.The
+/8000N,
ofvfauciyg*,/t isfft) =150o0
revenueearnedis a functionof the numberof units lhttarfl
sold:r(x) = 1000- 0.25x2.Find the function for
finddhe co6t as a
price,
p.
revenqgrr, in terms of the
Lru;
r(xq?) : l0c(,r* "zb (30 -zsp)
-
-
, Anlr
ILL'L; -.
z5noo*t4oc:P +6Zb.z)
-t9!1!1:jf!E:
ts6.LSe
f'_y:---\-*;:{J:-:J:.
=,
-35ap -!ru.:'59
*
/5',,z1;.)
l:+:,
;:_::"j
Ne,
Q/44*/
CCx)
= Q ' T + 2, ' 2 O t - G L l t z
w4u.*
lL-tl
lZ
Y
"
e hat
3 0 ) G r a p ht h e f o l l o w i n gf u n c t i o na n dd e s c r i b w
happena
s t t h e e x c l u d e vda l u e s .
e hat
2 9 ) G r a p ht h e f o l l o w i n gf u n c t i o na n dd e s c r i b w
h a p p e n sa t t h e e x c l u d e vd a l u e s .
3x +16
, ,- itr'L;i, ( t',-, ,/
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31) The regular price of a microwave in x dollars. Using a $5 off coupon makesthe price
.f (x) =x - 5. A 40%off salemakesthe price g(x) = 0.6..x. Which compositefunctionrepresents
;1- '
th e b e t t e rd e a l ?
*,i ,.,..,f1 :. /,,.. ii,,q,,;.t /' .i: .:- ;- ' ) ,r ;- ' ;,'
,i,
("f. sy\r)(g" /Xr)
/ti
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t't{''
t
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First take off $5, then take off 40oh
- First take off $5, then take off 40%
(t. iX,)- First take off 40%,then takg off $5
(g./X") -
First take off 40"/o,then take off $5
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