Math 1050
Exam 2 (Make-Up)
March 8, 2012
Answer all questions below. Every question is worth the same number of
points. You may use the available space for work, but must write ALL
answers on the answer sheet.
No cell phones, calculators, or nOtes are allowed during the exam. These
I
rules will be strictly enforced.
Name:
Number:
______________
flue or False: For #1-8 decide whether the statement is true or false. Write the entire
word “True” or the entire word word “False.”
1. a(b-i-c)=ab-j-ac
2. (x+y)7t=x7t~~~yTh
3.
4.
5. (zy)”
6.
7
\~y)
Vy
=
y”
0
8. —15x4 + 8x3 + Hz2
—
10 has 16 roots.
Alegbra
9. Findx where y’x+3 =7.
10. If g(z) is an invertible function, and g(4)
5, then what is g ‘(5)?
LI. Find the inverse of f(x)
o f (x) = x)
=
‘~
(
‘~/x + 3 + 7.
,ct3
12. What is the implied domain of g(x)
=
—
S-Sct~ ~
S
6
You can check your answer by seeing if
/
Page 2
5x? (Your answer should be an interval)
13. Find the quotient
)(
c’~~—
I
x4+15z3+2x
4-IS
j4-i-
15
3%c~-T
+
ist’+2z-~s
4
tS~-3~-3”
IS
-is-.
Sx...
14. Find the quotient
3\~
-2.0
6x3
—
jC)
20z2 + lOx
x—3
—
6
—L0
-‘
z
12.
1°
15. What is the slope of the straight line in JR2 that passes through the points (4, 5) and
(2, —1)?
S-i-I
Lf2
-
—=3
2-
Page 3
16. Complete the square: Write —x2 + 3x + 5 in the form a(x + 16)2 + -y, where a, ,6,7
)
c
2.
17. How many roots does —z2 + 5x
—
6 have?
~
~
≥roots
18. Find the roots of —x2 + —x + 3
—2-
19. Find arootofx3—x2—x—2
CAni.ck
Po.c~tvrs
°U~
±1) ±2
(~)3~(j)t
-(0-2
1-1- 1-a
<0
-~
2
e
JR.
20. (2 points) Completely factor 3z3 5x2 5z 21. (Hint: 3 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.)
—
—SE
-~j
LI-
:1-
O
—5~)L
~2\z
S
‘3
S
-,
DZ
2..
r
&
~
3x2#t+~
cx~sck—
1-’
4LL dtSCV1tfl’~flO~fl±~
(4~~Fo%c~4-or
3)(3xZ
L[(3~3)
<0
coeWjcjent:
OLLk
4 3
3Cx-3~(
3
:7-
2-1
X4~3
Page 5
Graphs
21. List all the monic linear factors of p(x) that you know from the graph below.
3
Z34
~(0
22. Graph f(x)
=
23. Graph g(x)
=
24. Graph Ii(z)
=
25. Graph p(z)
=
13(x + 1)2
—
~
Co
12 and label its vertex.
2\/x + 4 and label the y-intercept.
—
3 and label its x-intercept.
4x + 12 and label its x- and y- intercepts.
26. Graph the polynomial q(x)
=
3(x
—
4)(x
—
4)(x2 + 3). Label the x- and y-intercepts.
Page 6
Make-up exaw1
Name:
Number:
12.
3x
2.
FoJse
13.
x.4-t5~+
x3-L
14.
S
-i-s~ ~r
r
rocrbS
i
—
Lf(~
+
-l
oR
+
.11?
—2
-z
22. f(x)
24. h(x)
23. g(x)
C.-
—
it)
25. p(x)
26. q(x)
P14