1. Find the domain of the function 1(x) = 4x + 3
+
I and sketch its graph.
(-I
4
4
2-
EFzE2JH
Domain:
(write as an interval)
2. Find the equation of a line in slope-intercept form that passes through the points
A = (-7,1) and B = (-1,5).
—
2
=
-z
3
3. Given f(x)=
a.
(f
x
I
(go
g~
9,find
g)(x) simplifying as much as possible
(j,a
b.
and g(x)
A’
c~N~
9
t
[)(2) simplifying as much as possible
C
124\
z~47cE2r
‘5
6’)
Psrne I nf7
aJL
2x
Given j(x)
9
3
,find
f
(x).
K-
3
2ji-3
xbj-ñ
2~2
5. A graph, 1(x) is shown below.
(—Co
Domain of 1(x):
(state as an interval)
Rangeoff(x):
(state as an interval)
For what value of x does 1(x)
6. Completely factor x3 + 7x
synthetic or long division)
am
=
21x
~N~t
~__H_H
-E
3?
27. (Hint: -3 is a root; you may wish to use
(x÷2)) )é+?x2i2(xj~fl
•13
H
x?
4Lx2 ~I2A
a
i/t
4
A
9~
-4t
~LO~
0
9
Pciae 2nf7
7-
Answer hard to read. It is:
(x+3)(x+2-i*sqrt(5))(x+2+i*sqrt(5))
2x+ 3
Show and label its
x—1
x-intercept, y-intercept and asymptotes.
7. Graph the function: j(x)
—
i-c ~~;)
,)( i4
2xt3
~ 1400
‘:3
r
(a
ye’4
O~a~
S
‘Z
hor’~
8. Use the “completing the square” method to find write the
function, f(x) = 3x2 -12x +7 in the form f(xJ =a(x-hJ2i-k.
Then graph the parabola.
PocD~ 3(x2— ~x
t~
-2- ~
a
9. Solve forx
a.
116
I—
2
b. Iog~~=2
\2 S
XD
?~
-~
x
a
2Sa
(4
—
~9
/~N
Pioe lnf7
10. Solve for x:
x
(e9(e3”~2)
=
1
I
~<r2
-z
—)
/
QIlft~e.
)C
I
A / Sxr2~
j/~~
}-~
C
4x÷Z
x
-c
iN
1
fr~)(+2r6
11. Eliza has just started college. She wants to put some of her gift money in a bank account
so that in exactly five years she will have $2500 to spend on a graduation trip, lithe
account earns 4% interest compounded quarterly, write an expression (simolifv. but do not
evaluate it) for the amr
~f money Eliza needs to deposit now, if she is not going to
deposit ‘ny more me
.while she is going to school.
A~ P(i
$~ ccx
Szcw
~cbO
Hm)
F(o1)2°
+
—l
Lj
-
(1,01)20
-
7212. Graph the functions f(x) = —ln(x + 3) labeling and
showing any x-intercepts and any asymptotes.
e
Page 4of7
13. Solve forx:
ln(x+1)— ln(x—2) =Ln(x)
-
1’)
2<
)LFk
O~ x2-~x- I
?(~-
e.
eYA~
?c-H
)çeL
--N
Answer above missing
radical. Should be square
root of 13.
14. Solve the system of equations. Write the answer as a triple, (x,y,z)
x+y+z =3
x—2y+4z
=
3y +z
5
=
S
3!
-i-’h
2
csJ~
V.~
Cl
i-
~-
~-
2)
,c ~
t2..
15. Graph the inequalities and indicate the area satisfied by all of them by shading.
2x+y≥-3
—3
y≤3
x≥-1
16. Only two of the following matrices may be multiplied.
Write which ones (in the correct order!) and find the
Page Sof7
L
product:
A=[~
—~~1
©Ac
B=[2~1
z]
c=[~
.
•3
©
17. Let A
not
81.
~
=
[3
Find detA. Does A have an inverse? If yes, find it. If no, explain why
~(O~
~
~
-~
~
3Or’-f~
~2
Yes
SvCe
1
.
0
N
18. On Sunday, you receive seven cards. On Monday, you receive eleven cards. On Tuesday you
receive fifteen cards. If the pattern continues every day, how many cards do you receive on
the 50th day? If you save all the cards, how many cards will you have in total on the 5Qth
day?
s
St&~i.
T
a
~
4
-
-
~
~~cô
Page 6of7L...._—~
4-
19. Find the first three terms of the sequence:
9, 27, 81, 243
Write an
expression for the nineteenth term of this sequence (you do not need to evaluate it).
4-3
1
3
I
a,qUir
IC’-’
Icc
+1
17
20. Find the sum:
4
3
(:2
t
f
1_I
4-
4)
.=.-2,
21. Use the binomial theorem or Pascal’s triangle to expand and simplify the expression:
(x+y)6.
ci’-
5 5#
4
2
4-fl
2
/\\
1~~
4 4
6Ett
@
5##
||| 5
S
||||
‘3
C
I
2
13
tLt
Page 7of7
km
3
I
(~tf
to
ire
cc
~o
c
t
4
~
2?
U