MATH L3L Section 504 or 505
February 13, 20L4
Nome:
(printed ledgibly)
lnstructions: Do nat turn to the next page until I say 'BEG1N'!
7. Keep your eyes on your own desk (or on the ceiling).
2. show oll necessqry work to find your onswer.
3. Box in your onswer,
for work-aut problems
4.
5.
.',..',''.l..dfis.#ffi
lbo*#'**n',.om.ar:rlgi0J','bJ€'I'i.,...,
with severol steps.
calculator lids and cell phones must be in your backpock, out of view.
On your desk you may hove pencils, erasors, calculator (Mem Cleared) ond your photo
tD.
5. When finished, go bock ond check your work, with o careful eye.
7. When I soy, "Pencils DOWN', it means immediately. Points ore deducted for anyone still
trying to write.
8. use the bock page for any computations, but that page wtLL Nor be graded.
9' When finished checking all your work, close your exom packet to this poge facing up, ond
turn in your paper showing me your photo tD (lJniversity lD or Driver's License)
1-0. REPEAT: Box in your answer
for work-out problems
with seversl steps.
71_. Add your initials at the end of this line if you hove reod oll these instructions.
1_2. On my honor as on Aggie, I will NOT give or receive unauthorized oid on this exdm.
Signature
l-,U,C,k:!
:.'Do y6.u.r, br€Sti
r.
sorve for
o:E''lt = 256, given 3b-2c _3
(4-c
(hint: find a common
)
:
Express the domain of the function:
-f
3.
Find the difference quotient for the function: S
4.
Write
5.
as a piecewise-defined
function:
pts)
+ffi,
2.
(*)
base) (
ffiin
n(*):
* *:
(")
\ / - X-2
x3
interval notation.
(apts)
Show all steps.
(6pts)
-tl"l
ldentify each of the following statements as TRUE or
FALSE.
(4pts)
(4pts)
a. TRUE or FAISE Any number raised to the zero power is one.
b. TRIIE or FALSE 1n8x3 :31n2x
c. TRIIE or FALSE f (r) = 4x3 +2x has symmetry about the origin.
d.
TRIIE or FALSE A graph which passes a vertical line test, represents a one-to-one function.
6.
Write
a
function with a similar shape
toy
-J;
, which is shifted right 4 units, stretched by
factor of 2, reflected about the x-axis, and shifted down one unit.
7.
Given
f (r)-x*4, g(") -lnx and
n(*) -- e2'
, find
a
(4pts)
(g" h" fX")
(4pts)
8.
Find the inverse function, if it exist,
e.
Simplify: log, 8 + logs
+-
X
f(x)
* -?
-f(")
\ / - x+5
(4pts)
log 100
10. Using the table bel, find the best
best explains this
of
(4pts)
fitting model (LINEAR, quADRATtc, or EXpoNENT|AL) that
data.
(*\ =_
^. f
-2
-!
0
1
2
3
9.9
5.1
4
7.2
13.8
25
(2pts each)
Round coef
b.
to 1 decimal
Find the slope of the secant line on the interval
l-1,Zl
from the table above.
ffi:
x'-x+Irx<-1
Jx+z,-I r-a<z
/
oe
(aPts)
x-2
x-4'
Lz.Find rim
J f' +16
x->-3 x +3
-5
i-3. Find all asymptotes, and holes in the graph of
(apts)
f
(x)-2x-2
+ x-15
(3
pts)
x'+6x+9
to be made from a piece of cardboard, 16" by 20" by cutting equal
x inches on each
squares at each corner and then folding the sides up. lf the squares measure
L4. An open topped box is
(3 pts each)
side,
a. express the surface area of the box, S, , as a function of x. (does not need to be simplified')
s, (r)
:
b. Write the domain of the function using interval notation.
15. Jim leaves Boston at 6am driving to Chicago, arriving at 11pm, covering 1,000 miles. On the
second day, he leaves Chicago at 8am, and arrives at Lincoln, NE at 5pm after driving 540 miles.
The next day, Jim leaves Lincoln at 7:30am and arrives in Denver, CO at 3pm, after covering
500
miles. Round answers to 1 decimal place.
(3 pts each)
a. Find the average velocity driving during the three day trip.
b.
Estimate the time it will take Jim to travel the 4th day to Las Vegas, Nevada, another 750
miles, assuming he continues with the same average velocity.
16. Use the graph af -f
q
(")to
answer the following
uestio ns:
a.
l*
b.
f (0)
"f
(.)
c. l11 "f (.)
d. !gf(x)
(4pts
17. FebS'2O14:Avirusoutbreakhaskilled60,000juvenilesteelheadatRobertsonCreek
Hatchery and prompted the involvement ofthe Canadian Food Inspection Agency. Fisheries and
Oceans Canqda has confirmed that there was an outbreak of Infectious Haematopoietic Necrosis
(IHN) virus at the Robertson Creek Hatchery. gource: Alberni villey News) If the number of fish
infected was doubling every 6 hrs, how many days after the first fish caught the virus did
take to spread to 60,0o0 fish?
Round answer to 1 decimql placi.
it
(6pts)
(
17. Given
f
[to -3x2,r
Q) =1to*r(*+5),0<x <3
1""*t
a.
b.
o
(3pts)
rx)3
li1 f Q)
find liq f (.)
find
x+0x+3-
c.
18.
find ]i.q
f (.)
From the table of values below, find
X
2
4
5
f(x)
6
7
4
10
2
e(x)
7
10
2
4
6
19. Given
7
("f " s)(4)
(4pts)
10
n(*)- (" -4)t - x+ 6, find f
20. Find algebraically (no calculator) the
andg such
5x
lim
'6x+21
3x2
that n(*)
:
(-f " s)(")
(Show all work for any credit).
(4pts)
(apts)
f-z,x
2L. Graph .f
< -2
x'-r'-2{Y<2
(*)=l
\/
(4pt)
l-1'x=2
L*+l,x>2
3
i
i
:
i
i'
:
.......:...._.._.....
22. For each section below, describe what
is occurring in the graph of the given function.
a.
lll f (x) -rc and lgp f (") =*
b. g (r)
c.
,l1g
is not continuous over its domain.
n(r)-
4
round to 3 decimal places, where necessa
Pagel_/22pts
2A pB
_/
3
117 pts
4-11.6 pts
5_/15 pts
_/10 pts
Bonus_ I 1 pts
Grade on Exam L
(2pts)
(2pts)
B0NUS [4PTS) Use numerical approximation to approximate the slope of the tangent line
to the curve
y = J3* +l at the point (z,q). (minimum work to show: fill in at least the 1st & 3rd rows)
Page 2
Page
Page
Page
Page 6
(2pts)