Math 1050—4 Midterm Exam #2
March 13, 2015
• No notes, books, etc. are allowed.
• Answer the questions in the spaces provided.
• You have 50 minutes to complete this exam.
• Good luck!
Name:
uNID:
True/False
1. (8 points) For each statement, write the word “True” or “False’
(a)
vy
(a)
(b) (xy)’
1
(b)
=
(c) /j= /ç/
(d) a(b
+
c)
=
ab
(c)
+
ac
+
yfl
(d)
(e)
(f) (x
+
‘Ti
(g)
Algebra
1
x’
IeJ
(f)
U
IS c
(g)
+
2
6x
—
3x
+
5r
-ik
2 has 6 roots
f
2. (1 point) Find x where (x
standard form.)
(
up
ct
X
1X
(h) 19x’
1
=
T
(e)
(oj
y)fl
Ti
7)
01 C x
+
7)3
+
16
=
-[
(h)
1
(
i
s
LL
—11. (Your answer should be an integer in
+
ii
C
•-
(x
(?
2.
3. (1 point) If g(x) is an invertible function, and g(—
)
7
-
=
I(I)
=
4, then what is g (4)?
3.______
Points earned:
out of a possible 10 points
4. (1 point) Find the inverse of f(x)
seeing if f’ o f(x) = x.)
r
3
=
-7
\3
sJ)
3
3’x
—
5
7. (You can check your answer by
+
17
)(
7
c-(
c-5
)(-5
5=_
).3
<
‘
/5x
+
()
•r)
4.
5. (1 point) What is the implied domain of g(x)
answer as a set or an interval.)
5_-(
13
+
4
9x
—
S
2x
A,
Lw
(i-(k cfl’
(
)(<
C
C
fLJ
c
C(’(J
lj
1’? (Write your
j (&)
/
C, c
?CL(4)
[H
L
+
cJ
t(J
C
3]
5’
,_/
5. \_
C
I3/.
2
0 and that b
flt S
6. (1 point) Suppose that a
in standard form:
f—b
-
—
4ac
—
4ac
0. Write the folloring a an’integer
2
u
2
f-b
-
b2
—
xc
4at
2a
2a
4
YD°
()
Page 2
(‘
(A
IV&
I
xi
Points earned:
out of a possible 3 points
:t
1)5
ri
.4.
4-
>4
K
C
1’-
y’d
>4
----‘1-
H
fl
1.
00
c
.
.
.
-
H
-
-)<
q
L)
Q
C
H
—
v7
L
+
‘I
—
-
—.
—
I
-
-
LF
—
.
()
N
‘
-
s—
D
—
(1
-
L
‘-
÷
+
±
-
-
—
N
-
I ‘II
J
j
s_
L
I?
r
(J1
I
-
I—
-
A
-
-
1
—
-Q
(
—.
—‘
+
I
-
C ZS-
<
(
_—--n
4
ZcJ
.
‘
r
C
‘—
0
,
°>
J-
><
‘I
=
—
—
14. (3 points) Completely factor 2x
3 3x
2 + 2x 8. (Hint: 2 is a root.) (Your answer
should be a product of a constant polynomial (a number), and perhaps some monic
linear polynomials (monic i.e. the leading coefficient equals to 1). and monic quadratic
f 2 x
polynomials (which have no roots).
c ,P(K
a
(
C)C)(x2
a
; x)
C’
C)()x
2
i
k
12
K
—
3j .Q
1O
—
15. (3 points) Completely factor 2x
3 + x 5x + 2. (Hint: —2 is a root.) (Your answer
should have the same form as described in #21.) (L ci
f()
-
1
2
js c
LZZ-
a
2(a)
I
-
2x - 3
<
(.
ho
Page 5
i)
(
Points earned:
out of a possible 6 points
1)
Graphs
16. (1 point) List all of the
below.
monic
linear factors ofp(x) that you know of from the graph
2000
1000
2
-1
-2
-3
x
-1000
-2000
-3000
/
16.
‘4’
1°(C I(ra(
1A- C
‘7 () L’
(i
I
/
C
f}
/—
C’
x--)
Page 6
Points earned:
out of a possible 1 points
-c
33
17. (1 point) Graph 2
x + 3, and label its x- and y-intercepts.
1
7
4
r
((}
3
=
x
2
7
—4—2
(—,°)
2
4
—2
—4
18. (1 point) Graph —3x
— 3, and label its x- and y-intercepts.
-3
—k,
4
0
-3
2
—3
x
—4
—2
2
4
(c, -3)
—4
Page 7
Points earned:
out of a possible 2
points
— 1, and label its x- and tj-intercepts.
19. (1 point) Graph
—
(2
—4
)
.
-
4
2
—2
—2
/
j)
—4
20. (1 point) Graph 3(x
x-intercept.)
+ 1)2 +
1; label its vertex, and y-intercept. (It does not have an
A.
i
I
C-
4.
-
.
j
3()2
2
(I)
—4
2
—2
4
—2
—4
Page 8
)Z
1
-
Points earned:
out of a possible 2 points