Last Name:
First Name:
1.)
2.)
0
13.)
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14.)
—
3.)
15.)
ra€
4.)
2x2-1/x
L~
18.)
7.)
-r(~€
19.)
1-~rir’
20.)
—2
9.)
—7
21.)
3
22.)
10.)
—I
11.)
12.)
23.)
i-22
÷
U
t-tte
Le
-Sf,
~ 2Lf
6.)
8.)
3x2i2
3
16.)
17.)
5.)
2x2-3x÷q÷
x÷3
2
anti
i-~J~ii~~
x-2 X’~zi-Z
x÷Z
x~2
x÷3
24.) 2’Jx+l
26.) 3x+2
*
I,
S
S
I
~
-z
-z
—5
—$
-4.
-4.
25.) .~/!+1
a
2.3
‘t
I—I
2.3
1
t
27.) 3(x—2)2+1
If.
S
*
2
2
I
2.3
t
-S
I
$
I
•
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I
—l
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Second Exam
True/False
For #1-8 write the entire word “True” or the entire word “False”.
r1V~’/~=~
~YV
2.) (x+y)~=z~+y~
3.) ç/~=~Ø
4.) (xy)~ =
5.) ç’z+y=~+ç/~
6 •)
‘~
(X’jfl
\y)
—
—
29’
lilt
7.) a(b+c)— ab+ac
8.) 7x3 + 12x2 + 5x
—
4 has 4 roots.
*** *** ** *** ******** * * * * *** *** ** * ** ** * * ** ** *** * * *
Algebra
9.) Find x where (x + 4)3 + 7
—20.
—27
x..1+
7
10.) If g(x) is an invertible function, and g(3)
—
5, then what is g
1(5)?
11.) Find the inverse of f(x)
by seeing if f ‘of(x) x.)
3’~Yx
1
2. (You can check your answer
/
~~÷z
/
f-In
12.) What is the implied domain of g(x)
your answer as an interval.)
=
yZ)3
—
2 + 18x2
3? (Write
7x-2z0
Yx?Z
[24
13.) Suppose that a 0 0 and that b2
as an integer in standard form:
i—b— i/b2
2a
4ac\2
—
4ac ≥ 0. Write the following number
i—b— ‘lb2 —4ac\
+bt
2a
(3
I
14.)
Find
6x4
9z3
16x2—5x+11
3z2+2
z%2-3z
tc-t
3x2-’Z
-?x3 .+I2z~~ 5x÷I/
~3~3
j2x~.1 +1)
IZxt
-‘-S
1t3
15.)
Find
—2
2z3
2
7x2 + 3
x+2
—
-7
o
22
2-
‘-ii
3
~tJ.L(
22 ; -‘fri
16.) What is the slope of the straight line in 1112 that passes through
the points (4, 3) and (6,9)?
fib
‘7-3
2-
17.) Complete the square: Write 4x2 + 4x
where a,8,7 eR.
18.) How many roots does 3x2
2z
—
3 in the form cr(x +
j3)2 + ~
10 have?
‘f-lZO ccj
50
0
19.) Find the roots of x2
corsts
—
2x
—
10
z~zTTP
2(a)
1
=
I±ITP
20.) Find a root of 3x3 + 8x2 + 5a~~
Facto~5
oP
2
2
~ S(~2)t+ 5(-a)-F
3(-8)÷ S(tt)÷%z).z
-Z%t32- /0 -‘2
ZQ
a
CoG*.
21.) (2 points) Completely factor 2x3
2x2
8. (Hint: 2 is a root.)
(Your answer should be a product of a constant and maybe some linear and
quadratic polynomials that have leading coefficients equal to 1, and such that
any of the quadratics in the product have no roots.)
—
2
—
2-ad-B
o~
2xt+2x÷~
Is
2
2.
so
Lt’Q
tL
CoG~c ~f Pt-f
a~~-2x2- 8
/
( 2x.2~- 2z~’f )
(x
/\
2
(x~4-z~I)
22.) (2 points) Completely factor 2z3 + 9z2 7x 6. (Hint: -2 is a root.)
(Your answer should have the same form as described in #21.)
—
-2
29
-3
~i≤ci’°~t
7-6
≤
-10
2. 5 -3~ 0
2
~00~
-5÷~J~
2(z)
-5.u-7
-
-a
-I’
/
÷1)
(2zt
~-5z e3)
—5-7
Lt
2
(x÷~
(x-~)
LI.
* ** ***** ** ** *** *** * ** ** ** **** ** * ** ** ** *** *** ** * *
Graphs
23.) List all of the monic linear factors of p(x) that you know of from the
graph below.
~
—s
—z
-3
-~
—I
roo-F6-2
L~ 2
24.) Graph 2~x
I
2
5
_3
z~2, x -3
~acto(S
~jnctt ~gert
0
~/SkStISt1.
1 and label its x- and y-intercepts.
x-;~.~t• z&.,’~~.x~-i
y-nt~ ZTo.eu’:2
</~
25.) Graph
sta*4iC”
26.)
raph 3x
X~lritt
1 and label its z- and y-intercepts.
3k~~p~
x-~nt:&fTtg:o =!‘x~-2
2 and label its x- and y-intercepts.
3~+ZO
cS’)
1~t
X~ ..24
•
—int~ 3.042tZ
27.) ‘rap
2)2+ 1 and label its vertex. (You don’t have to be accurate
with the x- nd y-~ erce~
.
°rM ~
sk;V~
~
a
1.