Exam 2
-
Blue Version
Name:
/
There are multiple versions to protect examination integrity. Write the answers in the
underlined space provided. Each answer is worth one point, except #21 and #22 are
worth 2 points each. Partial credit is possible.
I
1.
12.
2.
13.
<-t
1
,
3.
4.
5.
16.
6.
17.
7.
18.
8.
19.
9.
20.
Cxf/)
—.
c
10.
21.((
V
3
-Lf
11.7
H I
J
8
23.
6<-I))
+
C4
—
C”
C”
C’1
C?
r
+
+
cI
L
C”
—
True or False
For # 1-8, completely write either, “True,” or, “False.”
1. a(b+c)=ab+ac
2. (xy)’
=
3. /ij= //7
4
3
5. 6x’ + 14x
—
20x
—
4 has 8 roots.
6. x+y=+j
/
7
\fl
(1
—
“ii)
8. (x + y)fl
v’
=
x + yfl
Algebra
9. Find x where (x + 9)3
—
3
=
5.
’J-w
2
10. If g(x) is an invertible function, and g(l)
=
6, what is the value of g’(6)?
11. Find the inverse of
f(x)
=
2’/x + 5. (You can check your answer by seeing if
f
o
f(x)=x.)
12. What is the implied domain of
interval.)
g(x)
10 + 2/9x
—
6? (Your answer should be an
)/ç;,
13. Suppose a
0 and that b
2
—
1ac
0. Write the following number as an integer in
standard form:
+b(_b__4aj+c
2
a(_b_2_4)
14. Find
5+4
4x
3x x
2+2
—2x
3
x
—
(1
lx
b
c:,)(
+
(-9
LJx
;
/
2-\
-x
1.
(
15. Find
3+2
—x
7x 8x
x—6
—
—
C
6
_c
-‘
—‘\
16. What is the slope of the straight line in JR
2 that passes through the points (—3, 1)
and (2,6).
L-C
-
—
z)
-
—5
32
17. Complete the square: Write
I
+ 6x
—
1 in the form a(x + fl)
2+
where c.
I)
)L÷
(-I
—
18. How many roots does —3x
2
—
llx + 9 have?
-“i -H(-N()
19. Find the roots of 2x
2 + 3x
—
5.
I
H
—
H
20. Find a root of x
3 + 3x
2
—
6x
—
8.
±
-3
)
-tc
o
-/0
01
e
R.
21. Completely factor x
3 4x
2 20x 7. (Hint: 7 is a root.)
Your answer should be a product of a constant polynomial and some number of linear
and quadratic polynomials that are monic, and any of the quadratic polynomials
should have no roots.
—
—
—
-LO
I
I
=
-3±d
22. Completely factor 3x
2 6x + 24 (Hint: -2 is a root.)
6x
3
Your answer should have the same form as described in the previous problem.
—
—
A5
3_
k
3
-
•2
-
L
CL
D [otc
LQ
frAØ
Graphs
23. List all of the monic linear factors of p(x) that you know of from the graph below.
24. Graph ‘%— 1 and label its x— and y—intercepts.
25. Graph 2/ — 4 and label its x— and y—intercepts.
26. Graph —x + 4 and label its x— and y—intercepts.
27. Graph —(x + 2)2 H- 3 and label its vertex.