Midterm 3 Review
1) Graph rn(x)
—2x(x
—
(x + 1)(2
3
3)
—
x)(x
—
PoOt
-\
1)2
((ii) (_2)
(
— I)
Also state the x-intercept(s), y-intercept, leading term (LT), domain
— -
“.‘
- -
c
xint(s):(O0.
LT: Zn
y-int:
D:
fy%
R:
—.
Where is m(x) >0?
..
3x
3
2
4x
x + 2 completely (Flint: x=1 is a root). Sketch the graph. Also state the
x-intercept(s) and y-intercept.
2) Factor f(x)
=
—
—
:)
L
—2
(-‘
zS ) 0
,:
°-
LQC
-(-LN
(O3((
X1flt()(0
.1oh
y-int:
1
(o
Z
4
f(x) x
3 6x2 4x + 8 completely (Hint: x=1 and x=-2 are roots). Sketch the graph. Also
3) Factor
+x
state the x-intercept(s) and y-intercept.
—
—
:j
?
-L
-
1
rI
\
::
\‘
e
-\&Cz
LT:
x-int(s):(
oN,
‘
q.
y-int:(O
f(x)
+ 3x j52 19x + 30 (Hint: (x+2) and (x-1) are factors). Sketch the
4) Find all real roots for
graph. Also state the x-intercept(s) and y-intercept.
—
—
——
r -l
—
L
-
Z-\9 —\r-SO
-
I!
I!
: :7::
-
‘—
\:
T
\re(-’, (o=
I
.1.• I.
x-int(s):
E2)0N (i
i
y-int:
2
(0
soN
F
(-l)(S)(
For #5-7 sketch the graph. Also state tile x-intercept(s), y-intercept.. vertical asymptote(s) (VA). and
leading t erm/enci behavior (LT/EB).
5) f(i)
2j2 +1
2
+ 1
coeme4e
ctc1zir-ed
-
-
&°
1.1
-
x-int(s):
I\) ove.
VA:
6)
--I
y-intO)
LT/EB:
\N
2
fr
-
z
d
4
3
2
f(x)
—
-LJ
(7
VA
3
7)
f(i)
=
Co-’-ee
x+ 1
r2 + x -6
e’x L_2
(—\ o
y-int:
x-int(s):
4 ctDr-e
c:’C
LT/EB:
VA:
For #8-11 sketch the graph. Also state the x-intercept(s), y-intercept, domain (D), and range (B).
8) f(x)e
—‘
o
x-int(s):
N
y-int:
R:
(o
(pcN
4
‘c
1
0
0
::::
r
—
—
r::::
.————
I
I
—
5
:
I
I
t
I
I
•
•
—
)1
z:j
2cbO
;
II
II
Zr
/
•
I
--
•
•
-
-
-
::L:
I
±“
-
HEE[:
-
E
4—
—
•
——.————
t::::::::
I
-
-i-
I
I
-
I
I
In
3-
r—’
3.
-
—
11
t
H1:
I
:::::::z
CD
—
4-’
0
ULN
I,
;
‘ii,
‘I
r
I_
—
JI,
If
aq0
.;:
-
If
—
—
o
0
(0
I’
A
—
I,
E1
N
(I
0
M
•
,-
LP
II
6
I’
‘I
—
I!
1’
—:-3
N
o
—
[0
N
i,j
II
C.(1
i
to
cc
8I
—
ULfl
‘I
LJi
II
Il
ii
I
c.,1
=
—
—.
CID
0
9,
0
IC?)
—
—
—
fr
*
..T::::::_
—
0”
El
0
0
3
3
0
t::::[
:--
Tt-—___Z.Z
4L
4—
H-----”-
::::
4 (1)
19) log
20) log
10 (10,000) =
21) 1og (e
)
3
22) log (32)
ZS
Approximate #23-25; state the integers between which each expression lays.
Loc)
1
23) log
2 (20)
aLL
\o3(Lj
39
24) log
3 (100)
L.
\O)L
25) log (30)
[ETco5(\oLS
‘
(i\I
3
‘
\ô
((
) D3 3>
Solve #26-34.
26) log
(x)
9
—
(x
9
log
—
1)
3
,_)c.
‘))i
4ex_ 7
27) 2
i1-2.
—
=
2
ie
t
r28) (223)
L
=
5(2x_2)
L
=Z
1
=5
7
=5
3
e
X
2
29) e
ex1
3-r(4
ThL.
(x
6
30) log
-\‘>
—
1) + log
(x +)
6
—
(x + 2)
6
log
2
0
rjl
(+
31) 9
(x—2)+1og
2
1og
(
x+1)3
0
L T&Nc
3
:
3
32) 1og
(x
10
—
1)_2
-5
4
=
flS-V
33) 3x
—
4
<
8
_c-j
-H L
L
12
34) 2x+3—58
‘3
Or
8
LJ
35) Graph
f(x)
—
x2
3—x
if x
if x
—1)
E (—cc,
E
ifxE
[—1,2]
(2,oo)
For f(x) above, find:
f(—2)
0
f(0)
f(2) H
36) Graph
f(x)
1 log
(x)
3
2X
ifx(—cc,0]
if x (0,3]
ifxE(3,oo)
For 1(x) above, find:
1::
f(3)rz
—
1a
4
9
I
For #37-39 determine how many solutions there are to each system and explain your reasoning. Then
find the solution provided there is a unique solution.
37)
5
Jx+y
f)c5
S’N(Q
k\Nc
S
(i+c
rc op€ o r-e
\- -€r-\#
38)
f2x—3y
y
1.
12
x—D
\2.
-
\2
E)
—-=-\•
8
fli\
[
Ta-
39)
•t’3
{::
9O
-iDr
S
r
-“33
me(e
(01
S
38
rn
H