MATH L3L Section 504 or S0S
Februsry 13, 201.4
Name:
{printed ledgibly)
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3.
Box in yaur gnswe4
for work-out problems
4.
5.
Answers baxed in and legible !
with several steps.
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tD.
6. When finished, go bock and check your work, with a careful eye.
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trying to write.
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9. When finished checking all your work, close your exam packet to this page facing up, and
turn in your poper showing me your photo lD (University lD or Driver's License)
i-0, REPEAT: Box in your snswe1
Answers boxed in and legible!
for work-out problems
wittl severcrl steps.
1_. Add yaur initials at the end of this line if you hove read all these instructions,
L2. On my honor as an Aggie, I will NOT give or receive unauthorized oid on this exam.
Signoture
1_
Good Luck! Do your best"
!,.
{hint: find a cornmon base} {4pts}
-Za.+43) *ffi
*u
)-l*tvb* = f
-2a+z(3u- ?-e-\=A
tF.
.-l
r
r.
ir
2. Express the domain of the function: /(x) = {F
.r-
-b.r+5=in
t*,{f{dio t,'t-t
1qJ-"r:afu6r-r't-*
CF'-qZo 5'{se
3. Findthediffereicequ6t-ienltoithefunction:
4.
S(x)=fr
\
{4Bts}
-- } 2-
,.
/
sr- t - \-.'r- r
$t\rh)=i##
;xt-wr"Fr*::;#fr_A
-(**NrL'*
-.
$1xr-h)-ft^)ztrhr+Ll -11S
r\(*3,t:-a
--S,
@,fe:-)-erdj
t tvlh+q}
>i:r'
. rr\
6. r\ $,.\ I --le
tj;jci:
;[
il
Jrr$rs${ ^,;ft;;s
Write
as a piecewise*defined
function:
*l Sro)= lt l
frx)
5.
interval notation.
ldentify each
i?-L, {Le>
** *l
X\ xdl'*
n{"}
= -rt -tltl
tno*altsreps.
.1
{
j!@following statements asTRUE or
.i
X t' 3
*$ Klm
K 1r{
FAIJiE.
Kc-s
6 t ,
riil;@ iny nrrb"r raised to the zero power one. C; t L
u. f
4 ortrake h8xr =3h2x G1xtz-.u = l^ (lx)
'ffi,
,
(*) = +f + 2-r has ,r*t*rry about the orie;. ,v$
,:ou, .,f
;:-
/ ,/
,,.:,,...':,-
{
h(K) -}xF\ X.;s ''€* 3v,
{
pot2l
(4pts)
is
- tl *t- zx =
d. rtue o@JA graph which passes a vertical line test, represents a one-to-one function. - (tl u-" r+
.r
5.
Write a function with a similar shape to y *
,which is shifted right 4 units, stretched by a
b*
factor of 2, reflected about the x.axis, and shifted down one
{apts}
J;
unit.
J;rffi
affi
#'=
*'ff*bffi ""xf
$s
7.
Given
/{*} =.,r*4, S(*) = lnx and *{*) = e2* , find {g" n" f}{t)
;"
,
f
\
i toft*?)
,\
"i
\d
i
T""-&,*ti
i
ft*t-*) i =
d*\..1*'
| ,,j ;
t4pts)
. (nr
^
a1,-+8
,
8'Findtheinversefunction,ifitexist,off{,}=#
s? L:&^
x+5
x: \/$ **2
.-fy, 4
{apts}
?:: SL t""*. *)
!-=,q,
5*t
l,*V .#
*[
\* o.*. S-K+Z
i-l +"s-
rr
.,1
tf
XS + $p 5*).-?
TF_;*
' 5x YZ3 ?J *K$
e. simptiry: log, 8+ lo9,l-611oo
l$
t
=
t
i
(apts)
Ti.2'
tlo:il
^42
=
10. Using the tabrq b{Tin! the best fitting moder (uNEAR, quADR4Ttc, fg#fi;ra., ,n}
best explaint *tBS"?!P
f (xl= 2 .0 y-f 1.6 X + {,t (2pts each)
x
-2
-1
f{x}
9.9
5.1
o
4
^.
1
2
3
7.2
L3.8
25
Raund caef ta 1 decimal
b.
Find the slope of the secant line on the interual
[*t,Zl
L'J
fr'' s,l)
#-, \3,s)
fronr the table above
.
rn
=.,. ?r$.
t3,8"**f. s ffi--"*
*
*kt]
dtF
3
,.
iI
,i
r$*
f.-x+l
sf*$"ts$#'I+{
idr-dtrl.
*"r-]*,-r*,
-j
(4pts)
ij
i C{*xF?-i
ce$ff
c,&T\*-#
\J
\"*}}qtu*
"*"_--*-$
i fik KF *$ i
lL. Find the points of discontinuity of
*
I.,-?
ba\ ]K#{
["-?'']a)
d-t F#-+'-
17
s, * 4 .ofr
2t
* *s
:
qi-*;ffiT*r #*= W*%,
.."
"^b
q-_"
r
1a, Find tim
fijf
r-+-3
X+3
Ap._gi
-"1
t4pts)
*x* *^b
5
y-z,q
&t
L*+t\
X*+
*{a
/
*"-U-,
d
.F
'l*
b4..dd'*
#
e.-Gd#*ag4*ebffi*'s
? +:rro *5
f {xr = ?It l.i - S
S*;,1qt"..+ JE{.AuAtn
13. Find all asymptates, and holes in the graph of
*"
$cr-,ta^s--
f *ry*-
$-}s-tlb t=z
{3pts}
j
L4. An open topped box is to be made from a piece of cardboard, 16" by ?0" by cutting equal
squares at each corner and then folding the sides up. lf the squares measure x inches on each
{3 pts each}
side,
a. express the surface area of the box, ,s,
s,
(')=
as a
functio:r:L
x( rr-2x\ t LyQ -r-)
-{*"
€''nas
?vlf **-"}-\
,:*
=
irr;:ffif,*rilied.)
#
b. Write the domain of the function using interval notation.
{-**?X 5#r lb*JX>&
K>o
t#pld"
qe t*
} "k}* .i
*l
;
q
<.r\
*"gs ='
Zxfo*-er)
X5. Jim leaves Boston at 6am drivingAChicago, arriving at llpm, cove14g 1,000 miles. On the
second day, he leaves Chicago
and arrives at Lincoln, NE q+dn after driving 540 miles.
The next day, Jim leaves Lincoln'bt 7:30am and arives in Denver, COat 3pm, after coyering 500
miles. Round answers to l decimal place.
{3 pts each}
{8.i",
a'
b.
:H,i:i'fHT':l
ff
-+'q
l?,5
driving
I
"'#:"{'.ff '1'ibto
AT*
tb,s
-=
Estimate the time it willtake Jim to travel the 4th day to Las Vegas, Nevada, another 750
miles, assuming he continqes with the $ame average velocity,
t?fo=
tF3. t)
ll,1 $*s,*3-l
16. Use the graph of f
(*)to
answer the following
questions:
(*)* 3
b. /(o) # 0
a.
l5p "f
m/{") =/
d. |g/t') : -l
c.
(4pts)
60,00A juvenile suelhead at Robertson Creek
Hatchery and prompted the involvement of the Canadian Food Inspection Agency. Fisheries and
Oceans Ca4ada has confirmed that there was an outbreak of lnfectious Haematopoietic Necrosis
$HNJ virus,atthe Roberhon Creek Hatchery. {source: Albernt Valtey News} If the number of fisb
infected was doubling every 6 hrs, how many days after the ffrst fish caugbt the virus did
take to spread to 6O,0OO fish?
Raund answer t0 L decimal place,
L7. Feb 5,2011,4: A virus outbreak has killed
N= fia
* zryu
{nss*
- ) x;:.,
J-futa0-S0D
*n^ &D,o
g
--*-**L
#-
aos &'-*''^L
t$'qffiff
.6F L
.#u
& tS, 2xt* h.s
&
3,\uvttf C*p*
ru* nL4$tubes **w
f1; | :2-* 4*e
{* to blu
ft= 2o
t*fi*'2f**
3
tS t%la
b:
{?*
fix.S
:' 3-$}'L
2*
tls tf#*at {*
n3
r,
tf
L
2*
Jlp
?_
fffi
it
fto
*3xz,x {
f {*} = J losz(x + 5),0 s x s 3
17. Glven
l"'*t, )
tr
a. find
]gp/{') :
b, find riq
x+3
c.
o
find
f (*) +
lim,/{r)
aA
(3pts)
3
L
to -3(CII= tO
ry*{3 r 5}*"[.knr{s)x $
to *-?
t*nroS =
18, From the table of values below, find
x
2
4
6
7
L0
r{x}
6
7
4
2
etx)
7
L0
2
10
4
6
*fs
{f ,gX4}
t [,t\ =
{4pts}
to
$,,b)-El
=(r-4)' - x+6, find /and g such ttrat ft(r) = (f 'S)(t).
htx) =
rc,t f +2-
19. Given
ft(.r)
-)'e+z
(-*-uJ-$-+)
ht,)=
-/
r\-!'li'*,q Cx)'__\:3
20. Find algebraically (no
t4pts)
_)
calcutator)*",H#
(show ail work for any credit).
ruvn JJgr-"C
\A-N Uy- f L\ =!:.*)-k"t
,11*)
{4pts}
t*i
{"-""-*-"--*-"1
tri,"*W
r{
--***.- }
i
l-t'x
Graph
L.
< -Z
f (.)=j:;'::Sx
<2
(4pt)
I
L*+1,r >z
22, For each section below, describe what
is occurring in the graph of the given function,
a,
]gf f
{*) and }gp f {*)= ff
Uuttil",r Cr6rry*\- &q
ck K.* t
{2pts}
{T\r\.
U.
S(t)
is not continuous over its
domain.
(2pts)
tL hos sttheu a.gap,
d*"vp, *r, tre,rtti,s.t*%*pt5h-
c.
n{*}-g
,,$1
honL3ftsr'$s^r-
BONUS
[4PTS)
x
v
ffirQ
2,1
*?,
2,qq
. (minimum work ro show: fill in at least the 1sr & 3rd rows)
ttL{vs 3 gqe?yl
round to
CI 3 decimal
ma nlaces,
wh
necessa
?c,,.P*F' ,ySqle
a,qqsf
,m Sq#&t
r4
3
Si fstrr .TTf r* ,3?s
f-rt.3*t{
Pagel-/22pts
PageZ. _- , / 20pts
Page 3
Page
&S Bffi 4
Use numerical approximation to approximate t}re slope of the tangent line to the curve
at the point (1, q)
y = Jif,i
{2pts}
_/L7 pts
116 pts
Page 5- , . _.._ 11.5 pts
Page6 ,,* flOpts
Bonus... /4pts
Grade on Exam 1
t:
3,e al l3_Ol
s*l
4,0 oe37*I {,ss3tt,4f 4,a3:3
*#fls .3i r{8 ,3?$ aE
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