Exam 2
-
Yellow 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.
12.
1.
7 ))
L
In
2.
13.
3.
1
4.
15.
5.
16.
6.
17.
—
(1
—
(_LS_
I
7.
18.
8.
19.
9,
20.
)
2
c/
21.
J
-
22.
23.
k
<-O)
(L)
+
fD
H
I
II
c.q
+
I
S
—
I
C
True or False
For # 1-8, completely write either, “True,” or, “False.”
1
•V”
/
2 (
3.
\fl
=//j
4.
5. (xy)’
=
6. (x+y)=x+y
Th
7. 7x
—
2 + 3x + 4 has 4 roots.
8x
8. a(b+c)rrab+ac
Algebra
9. Find x where (x
—
6)
—
10
—2.
JT
10. If g(x) is an invertible function, and g(7)
=
3, what is the value of g’(3)?
11. Find the inverse of f(x)
=
2/+ 8. (You can check your answer by seeing if
f(x)x.)
f
o
y
12. What is the implied domain of g(x)
interval.)
(o
=
14
—
5/1Ox
—
6? (Your answer should be an
-
13. Suppose a
0 and that b
2
standard form:
—
4ac> 0. Write the following number as an integer in
14. Find
x
3x
2
2
+
5
4x
—
4
+
0
9
I
2-
-
(
‘k
-6x
*
6
X
8
+l°X
15 FjndX+
x+6
Ic)
—‘7
c
2 that passes through the points (2, —3)
16. What is the slope of the straight line in 1R
and (6,—i).
-
17. Complete the square: Write 3x
2
‘V
—I--
-
2.)
—
6x + 8 in the form ci(x + 3)2 +
—
—
(—c)
I
-‘
18. How many roots does 2x
2
U
—
lix
—
8 have?
-
19. Find the roots of 2
—3x + 2x + 5.
±
-
-c
20. Find a root of x
3 + 3x
2
1
3
—
6x
—
8.
where c,
,
E R.
21. Completely factor x
3 + 8x
2 + 19x + 20. (Hint: -5 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.
8
Is3
Cf
2
7
Ytc
x
t)XL1
22. Completely factor 2x
3 + 4x
2 lOx 12 (Hint: 2 is a root.)
Your answer should have the same form as described in the previous problem.
—
2
q
—
Io
‘V
Graphs
23. List all of the monic linear factors of p(x) that you know of from the graph below.
-6
3
24. Graph ‘/—x + 1 and label its x— and y—intercepts.
25. Graph —2/ + 4 and label its x— and y—intercepts.
26. Graph x +
27. Graph (x
—
and label its x— and y—intercepts.
2)2
—
3 and label its vertex.
4
5
6