Last Name:
First Name:
1.)
13.)
2.)
14.)
3.)
15.)
4.)
16.)
5.)
17.)
6.)
18.)
7.)
19.)
8.)
20.)
9.)
21.)
10.)
22.)
11.)
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Graphs
23.)
12.)
22.)
23.) List all of the monic linear factors of p(x) that you know of from the
graph below.
p&c)
1
it
√
√
33 √
3
23.)
+
2−121− 1
24.)
−2
23.)
−2
x−2)
36.) −3(xxx+
√
3 √
3 32
25.)
−3x
26.)
2x
−
23.)
x+
+
2−2)
25.)
2x
−
32)
21 2 − 1
23.)
−2
x+
36.)−3(x
39.)
f−3(x
(x)
36.)
+
−1
25.)
−3
25.)
39.)
36.)
39.)
f
√√
√
√
3 √
25.)
−x
12−1121
24.)
−
xx−
+
37.)
p(x)
24.)
−x
23.)
+
23.)−3(x
−2x3−
36.)
+
2) − 1
√
√
√
2+ 12
3 √
37.)
p(x)
27.)
−3(x
2)
26.)
3(x
+2−
1)12)
3+
24.)
−
xx
1212 −
40.)
g(x)
26.)
−3(x
+
37.)
p(x)
2−1
24.)
−x
25.)
23.)
−3x
x
+
+
2
22)
23.)
25.)
−2
2x
−
3
−
36.)
−3(x
+
36.)
39.)−3(x
f (x)+ 2) − −
1 1
40.)
37.)
26.)
40.)
g−
26.)
25.)
−3
25.)
36.)
39.)
39.)
f−
√√
38.)
q(x)
24.)p(x)
−−xx−
+11
37.)
24.)
√
38.)q(x)
q(x)
√
38.)
37.)
p(x)
24.)
26.)
−
3(x
12 2+−2 1
37.)
40.)
p(x)
g(x)
24.)
26.)
−3(x
−xx+−
+1)
12)
38.)
37.)
40.)g−
p
26.)
40.)
26.)
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Graphs
22.)
23.) List all of the monic linear factors of p(x) that you know of from the
graph below.
p&c)
38.) q(x)
2 22
12
22
12 12
38.)q(x)
q(x)
38.)
it
38.) q
Second Practice Exam
True/False
For #1-8 write the entire word “True” or the entire word “False”.
1.) a(b + c) = ab + ac
2.) (x + y)n = xn + y n
√
√
√
3.) n x + y = n x + n y
4.) (xy)n = xn y n
√ √
√
5.) n xy = n x n y
6.) ( xy )n =
q
7.) n xy =
xn
yn
√
nx
√
ny
8.) −x4 + x3 + 17x2 − 3x + 4 has 7 roots.
************************************************
Algebra
9.) Find x where (7 − x)3 + 4 = 12.
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Graphs
22.)
23.) List all of the monic linear factors of p(x) that you know of from the
graph below.
10.) If g(x) is an invertible function, and g(2) = 7, then what is g −1 (7)?
p&c)
3
it
11.) Find the inverse of f (x) =
seeing if f −1 ◦ f (x) = x.)
√
3
2x + 4. (You can check your answer by
√
12.) What is the implied domain of g(x) = 2 2 5x + 1 − 23? (Your answer
should be an interval.)
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Graphs
22.)
23.) List all of the monic linear factors of p(x) that you know of from the
graph below.
13.) Suppose that a 6= 0 and that b2 − 4ac ≥ 0. Write the following number
as an integer in standard form:
−b + √b2 − 4ac −b + √b2 − 4ac 2
+b
a
+c
2a
2a
p&c)
4
it
14.)
15.)
Find
4x4 − 6x3 + 2
2x2 − 1
Find
4x3 − 5x + 6
x−2
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Graphs
16.) What22.)
is the
themonic
straight
line factors
in R2 that
passes
Listslope
all ofofthe
linear
of p(x)
thatthrough
you know of from the
23.)
the pointsgraph
(2, 4) below.
and (5, 10) ?
p&c)
5
it
17.) Complete the square: Write 2x2 − 4x + 5 in the form α(x + β)2 + γ
where α, β, γ ∈ R.
18.) How many roots does 2x2 − 6x + 10 have?
19.) Find the roots of −2x2 + 6x + 2
20.) Find a root of −3x3 − 7x2 − 4x − 4
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Graphs
22.)
23.) List all of the monic linear factors of p(x) that you know of from the
graph below.
p&c)
6
it
21.) (2 points) Completely factor −2x3 + 6x2 − 2x + 6. (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.)
***********************************************
Graphs
22.)
23.) List all of the monic linear factors of p(x) that y
graph below.
22.) (2 points) Completely factor 2x3 + 11x2 − 20x + 7. (Hint: -7 is a root.)
(Your answer should have the same form as described in #20.)
21.) (2 points) Completely fa
(Your answer should be a prod
quadratic polynomials that hav
any of the quadratics in the pr
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Graphs
22.)
23.) List all of the monic linear factors of p(x) that you know of from the
graph below.
√
√
3
3
23.)
−x
x+−2 1and
andlabel
labelits
itsy-intercept.
x- and y-intercep
24.) Graph −2
p&c)
√√
24.)
x − 21 and label its x-intercept.
25.) 7Graph − −x
x- and y-intercept
it
25.)
andlabel
labelits
andCompletely
y-intercepts
26.) Graph −2x
2x −+3 4and
x-x-and
y-intercepts.
22.)
(2its
points)
fa
************************************************
Graphs
22.)
23.) List all of the monic linear factors of p(x) that you know of from the
graph below.
p&c)
it
√
√
3
3
23.)
−x
x+−2 1and
andlabel
labelits
itsy-intercept.
x- and y-intercepts.
24.) Graph −2
√√
24.)
x−
25.) Graph − −x
− 21 and label its x-intercept.
x- and y-intercepts.
25.)
andlabel
labelitsitsx-x-and
andy-intercepts.
y-intercepts.
26.) Graph −2x
2x −+
3 4and
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2 2
Graphs
27.) Graph
−3(x
1 andlabel
labelitsitsvertex.
vertex.
26.)
5(x
++
2)2)
+−
1 and
22.)
23.) List all of the monic linear factors of p(x) that you know of from the
graph below.
p&c)
8
it