Math 1050-003 1\/Iidterm 2
Spring 2016
Name:
So\&to
UNID:
• SHOW ALL WORK. No points will be given for answers without justification.
• The more you show you understalld tile material, the more points you wiH receive.
• If you are using a formula to complete a problem, make sure you write down the formula first.
• Simplify your answer as much as you can without a calculator.
• Make sure your handwriting is legible.
• Put your FINAL answer
ill
the space provided on tile exam so that it is easy to locate.
• Calculators, homework, notes, phones, or any other external aid are NOT permitted.
• Absolutely no talking is permitted during the midterm.
• Be sure to work carefully and check your answers before turning in your exam. Once an exam has
been turned ill, you will not be allowed to alter your exam for any reason.
• Good Luck!!
Math 1050-003
March 3, 2016
Page 2 of 10
1. (4 points) Simplify the expression completely:
-
Zr
x+ 1
2x-1 3
/
\
/Z
/
)Laic-’
-)
-
-]
L
(1)
2. (4 points) Simplify the expression completely:
(3x2)
(3)
(N
=
2.
(2)
3. (4 points) Solve for x:
x
+
2
5
—1
2 + 3x + 2
x
—
2
(3)
9
Math 1050-003
Page 3 of 10
4. (6 points) Below is the graph of
(a) Explain why
f
f
: 0,
)
—*
March 3, 2016
(—, 4].
is one-to-one.
s .ses te
(b) Explain why
f
‘1\e
4e.1-
is onto.
ce+
Tr
of
6
s
f is both one-to-one and onto, f has an inverse. Plot the inverse on the graph
above. Be careful to accurately plot the coordinates of f
.
1
(c) Because
Page 4 of 10
Math 1050-003
5. (6 points) Find the inverse of
March 3, 2016
f(x)
=
-s=
(5)
6. (6 points) Solve for x:
2(x + 5)3
—
9
=
7
(6)
7. (6 points) Solve the inequality for x:
—3 + 1 > 4
9
(7)
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March 3, 2016
Page 6 of 10
Math 1050-003
10. (6 points) Find the quotient:
3
6x
—
2r + lOx
2
2+3
2x
—
8
-.-
2
Zr$
-
(10)
+
11. (4 points) What is the equation of the linear polynomial that passes through the points (3, 5)
and (—1, —7)?
s\oçe
-
(11)
Page 7 of 10
Math 1050-003
12. (8 points) Let
f(x)
=
—
(a) State the domain of
March 3, 2016
+4
f(x):
(12a)
(b) State the range of
f(r):
(12b)
(c) Find the x-intercept(s) of the graph of
0=
f(x) (So\e
4L1
(d) Find the y-intercept of the graph of
(12c)
3I
(12d)
(o
f(x)
(e) Graph f(x) accurately by using its x- and y- intercepts. Be sure to label at least one
point on the graph.
F
—
—
—
p
—
—
—
Math 1050-003
Page 8 of 10
March 3, 2016
13. (6 points) Complete the square: Write f() = 2x
2 12x + 13 in the form a(x + )2 + where
a, , 7 E R. If using a formula, be sure to write the formula first. If deriving, be sure to show
—
every
step.
a
(- &Y=
i
2
(13)
—
S
14. (4 points) How many roots does 4x
2 + 3x + 1 have? Justify your answer.
Dc
—
L
c
-
9—\to —O
(14)
N
ea’
rootS
Math 1050-003
15. (8 points) Let
Page 9 of 10
f()
=
—
1)2
March 3, 2016
9
(a) State the transformations applied to the original function x
2
1. 5- r\* I
2.E\\
_(,-,‘
9: -(-÷
(b) State the vertex of
f(x):
/
(15b)
(c) Find the x-intercept(s) of the graph of
0: j-9
f(x) (So\u
--o(
11.
&)- -‘1
a
(15c)
(d) Find the y-intercept of the graph of
f(x)
co r
(15d)
(e) Graph f(x) accurately by using its x-intercepts(s), y-intercept, and vertex. Be sure to
label at least one point on the graph.
S
/
16. (4 points) Find a root of p(x)
=
3
2x
—
2
3x
—
—
2 and verify that it is a root.
c-s c- -z:
?(‘ Z--\-2
y(a= -2-2
(16)
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