Wbek in Review
DROST
MATH 131
Algebra Review,
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1. Algebra Review
a) Simplify: 16-*
b) Factor: 3r2 - 5r
c)
-
ffi*)pr% ;ffit
2
.$
J'
Simplify:
L { n1-3 - 1x;
d) Simplify,
i.w
ii.
ffi
e) Multiply and sirnPlifY:
(3*
-
2)(",+
e@-*
.*rlgrF4
4)
f) Factor cornpletely; t;4 - 6ra * 9rz
}c
S) Tonya had one-third of the problems finished before dinner. After dinner she completed
8 more problems, and then took a break since she
wa5 half way done. How many problerns were a^s*
{w
w
r."1
&
signed?
f
h) Simplify
rs@
t't
\
lr.tu )
comPletelY:
fin
2r2
-7r-4
n2-7n*LZ
t
u_e
S,
2. Finding the dornain of the function
- \fr ' nz - 4r * r
b) /(") - iFT
c) J(c) -fiq,
") f
(*)
_
r*5
d) f (*):
e)
/(r) -l r
r) /(*)
3.
I
,ffi
- r*t
Be able to express youf answer in each of the
following forms:
Interval Notation
a, [-4, 3)
b.
c. (-*,2]
4.
tf.
,r'*a\
t/
#+"i$ {,#
ffi h*-
Inequa,Iity Notation
-2<r15
&
*{u
Find the average rate of change between the fol-
L*""**
lowing sets of points:
a.
: 4 ft;
Y: Y_h i
.b.flD
-3) and (5' 2)
b. (n,b-1) and (a- 1,b+1)
(8,
h
rstr'
'"r-*iXS
s-s
t,
2o) R,
#
V/eek in Review
MATH
131
DROST
Algebra Revi€w,
b) R
1
c) f-
1.1
47t>
XL
1.
Algebra Review
*f
)df )cao K
dl
a) Simplifo: re-?
b) Factor: 3rz * 5r
-2
I
c) SimPlifY:
I v -3 " T
r*3
d) SimplifY:
i.
ii.
tr
e) rR,
e) Multiply and simplifY:
(3*
f)
-2)(r+a)
Factor completely: 14
*
6113
*
9rz
g) Tonya had one-third of the problems finished before dinner. After dinner she completed
8 more problems, and then took a break since she
vra,S half way done. How many problems were assigned?
h) Sineptify comPletelY:
2r2-7n-4
nz *7riL2
2.
Finding the domain of the function
a) f
b)
("):
* 4r + 1
v€ - nz
f(*): ffi
c) f
yrl+o
h XtS-lo
y{-l
,( z -{)
7D) -q L, y,e.J
b1 t2rf)
e) x3z
tf . ou$ tqfr-
o)
("): !Er=
'f
(s r'3)
D ta, b -t)
r)
3.
VYL?
f(*): 'tr+6
n*l
Be able to express your anslver in each of the
following forms:
lnterval Notation
a.
Inequality Notation
l-4,3)
b.
c.
4.
(**,21
-2 < r S 5
Find the avelage rate of change between the foL
Iowing sets of points:
a. (8, *3) and (5,2)
b. (a,b*1)*d(o-1,b+1)
ol\\A (a--(>btt)
5.
\Mrite the equation of the line passing through the
point (5, -2) that:
a. has an ,x-intercept of
b. that
passes
2.
through the origin.
c. that is horizonteil.
6.
Identiff each of the following
funaions, or neither.
as even
functions, odd
a' Y=x2+5
b. x2+t'=+
c'
7.
v=l
{EdF
Graph: y= (x-4)t +
ss.i$}
wta
n
4*
:1'
LI
@F'6 i'* '
*'
i3il
f
'..,i
5
r#16
\d.
,1fl''u
i
i
I
I
_
8. A right rectangular box has a volume of 320 in3-
- -'!
If
the length is 2 in. more than the width, and the depth
is haHthe width, write an equation (DO NOT
SOLVE) to represent this information.
9. The amount spent annually in college bookstores
in the U.S. is modeled by
f (")
- .t9r + 1.6
where r is the number of years since 1982, and
f (") is the amount spent in billions of dollars-
a.
How much is the spending increasing
*ff
bJ
fo u#
t
@ d-,*
a&tskd
v e"_$"*
fi"&"'
b.*-
"+,-#
**qJ m
each year?
b. Acc.ording to this model, how much was
spent in 1990?
:
10. Given f (*)
'nz
h(") :n2 -16a. Find
-
6rr
*
8,
g(r) - 6-8,
nri
and
(f - h)(t:) and state the dornain.
*r,,il
qJ*r$L
f
f;
b- Find
(f) (r) a'd state the dornain'
c. Fincl
(l) ,",
11. Given: 4r
*
2y
-
and state ttre <lomain.
30. If
the y value changed?
r
increa^ses 2a',
how is
*ar_ry
&-w
5.
Write the equation of the line passing through the
point (5, -2) that:
a. has an x-intercept of 2.
b. that
pas$es through
the origin.
c. that is horizontal.
6.
Identiff each of the following as even firnctions, odd
functions, or neither.
a' Y=x2+5
b. x2+t'=+
c- rI=1
7. Graph: y= (x-4)t + 5
5=x
8. A right rectangular box has a volume of
320
in3.
If
the length is 2 in. more than the width, and the depth
is half the width, write an equation (DO NOT
solvE) to represent this information.
V z L. tt . ol,
d
ln= '[ q bitttotu c(o(a'tf
9. The amount spent annually in college bookstores
' in the U.S. is modeled by
/(s):'19tr+1'6
where r is the number of years since 1982, and
f (*) is the nmount spent in billions of dollars,
a.
How much is the spending increasing
each yeat?
b. According to this model, how
in 1990?
much was
spent
: trZ * 6n+ 8, g(*) : {g;Ar, and
h(n):t2*16'
a, Find (f * h)(") and state the domain.
10. Given f (")
b- Find
(*) ,", and state the domain'
c. Find
(:)
11. Given: 4n t 29
@) and state the domain-
:
30.
If r in
lo.
$tx)? f-(er'+8
y-Z
l^, u\ --
guD
=
l(p
-t|I
3 -bY "{-7+
f
12. Name four ways to represent a function'
qqot)= gO -6u:u*\'_;l rol
h
!3.
--' Find the average rate of change for
I6l--ir2
2 and A'r
nI- f when n -
:
4'
14. solve the following double inequality for
r:
2r-4536<5r*TI
15.
\\.
e 5Y+ l)
3Q
4
2x-4
ssion which rePresents the
of the basic square root function wit
iv-
<,y
the following changes:
5)
a. shifted left 2 units,
b. reflected about the x-axis,
c. shifted uP 3 unit$'
1y9
l{,o) ,r, ?.[ffi
16. Basic Eleruentary Functions
1. f ("):
z sqr) *
&
b)x
c)
Column B
Column A
a. shaped like
nt-
,/i
:2*
5. G(r)
* {n
\r'
b. increasing function
concave up
h(r):l "l
4. F(")
a, "
c. parabola which oPens
d. half a Parabola whtch
opens to the rigtt!_
e. increasing tunction
J.hL$: t*l o
A-ruD = t-.-
concave down
L7, Graph the piece-wise defined function
/(r): t ;::t,n' ::?
18. T or
F:
d0.) =\tV
x=Arepresents a function'
Lg. Given the parabola:
+3
f (")
*
a. Find the domain of
3r2
*
LZs
+ 2'
f (")'
Iq.
b. Find the rang€ of /(")'
1 r.r
c. Find the vertex.
g(") :4(r * 2)' + 5
a. Find the r-ittercePt'
b. Find the YintercePt'
c. What is the axis of sYmmetry dg(x)?
20. Given;
21. Find the equation of the parabola which opens
up and has a vertex at {2, -3), and' passes
)e
t
It. $a\g r.lq. e)
b)
through the Point (4, L)'
Uer.t<v
*T
e
is fto"Do)
2o.
12. Name four ways to represent a function.
a. ugrbebt
b. YLtr t qeLr
)tK)
7 .,1
J**
h
c.
..-5.
d.
F r{ LK.-
f(r)-3r2-r+Swhen r- iu"d A,r-
14- solve the following double inequality
2r-4586<br*11
4.
hu
for
e:
bf -t
b. reflected about the x-:txrs,
;hifted up 3 units.
1. f
(") :
-l r
4. F(") :2*
3. h(")
5.
17
c(r)
d. half a parabola which
- fr
opens to the right
e. increasing function.
concave down
f (")
:
a. Find the domain of
b. Find the range of
c. Find the vertex.
Jr2
-
asoes 5
f
LZr +
2.
t<
f"
f (").
f(").
O.L)L-
"Y
v3
* r{q,
lr&-
r{
g(r) :4(n * 2), + b
a. Find the z-intercept.
b. Find the gr-intercept.
c. What is the axis of symrnetry
(q, D
-'' t'
€?
\p cL ,"$
2A. Giveu
b
of g(x)?
21. Find the equation of the parabola which opens
up and has a vertex ufr, (2,
-3)o and passes
through the point (4, I).
-t)
t4:
0t
x=4 represents a function.
19. Given the parabola:
et . \) e^trr, 2)
{,i T*
::i
f(*): { ;?:in,
F:
Y-f'ry
concave up
c. parabola which opens up
- Graph the piece-wise defined function
18. T or
r.i {zr
r) }
L
b. increasing function,
I
Pb.,
'(_n'b
UgrtL'y*o
a. shaped like a " f'
trZ
*_*
4S
n K3 c
c) o \L\s o$ SSr*.$ngqX
I
Column B
* {i
LY-'A'
3L\
16, Basic Elementary Functions
2. s(r)
L
) :'t(*
z ,r{+.f
F 1 +-r
a. shifted left 2 units,
Colurnn A
eo
t..ceft
rJ
15- write the expression which represents the
transformation of the basic square root function with
ttre following changes:
?_
*(K*
13. Flqd the *verage rate of chanse for
z
= I(x-z) -3
"l*2"
Find the difference quotient for the function
f(x) listed in problem #13.
St,
+-5
d X*I-LP 5
V-[r" *-f
23. Which of the following are polynorrials?
a. 3n-2 * 4r
- 12
b. rr3 *4r -2
c. 4{i+5
2tr + 10
ti',
T(*F\
-$cD= 3 Y'+blc 1.,+ 3*-*Y-Lr+I
43a y,
r_ b
= byh, Y 3lJ
74. Solve for x:
a. 3o*2
_ |S5-r
b. 25 * 5' :53n*a
h-
L-
:25A 3io'tt1.
a. If a student does nbt-study, w-hat does this
bv the function iV
b'v- +*SVL
model predict their score will be?
be?
I
studying approaches
infinty, what does this model predict their score
will
'
bYt\+-3Lt--h..
25. If t represents the time in hours spent studying
for the exalll,and the a,verage score is described-
b. If the time spent
+5)
23. b,
zq. BYIL
: rf-)'
=
3y+b = LO *49
= 14
7-= L
T>e
"''2 aJv
-l =y
25"
,- ^*D,l
25( Ll- 3t
.g
)5c\ ), {)
!:&5[4€3)
N --
b)
f{=
N=
N=
ioD