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2B · Unit 2B Review
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Unit Review
21
Unit CA
11
Worksheet PDF
Reveal all
1.
f
(
x
)
=
3
log
2
x
+
8
f(x) = 3\log_2 x + 8
f
(
x
)
=
3
lo
g
2
x
+
8
. Find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
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2.
(Calculator) Solve
4
⋅
2
x
+
5
−
10
=
22
4\cdot 2^{x+5} - 10 = 22
4
⋅
2
x
+
5
−
10
=
22
.
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3.
Find all solutions:
ln
(
x
+
10
)
+
ln
5
≤
ln
(
2
x
+
17
)
\ln(x+10) + \ln 5 \le \ln(2x+17)
ln
(
x
+
10
)
+
ln
5
≤
ln
(
2
x
+
17
)
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4a.
(Calculator) Rookie card value after games played. Find a logarithmic regression model.
Games played
1
3
4
9
Value ($)
57.50
37.77
32.74
18.55
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4b.
How many games until the card is worth $10?
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5.
a
,
b
,
c
>
0
a, b, c > 0
a
,
b
,
c
>
0
. Expand:
log
(
a
5
b
2
c
3
)
\log\!\left(\dfrac{a^5b^2}{c^3}\right)
lo
g
(
c
3
a
5
b
2
)
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6.
(Calculator)
f
(
x
)
=
log
3
x
f(x) = \log_3 x
f
(
x
)
=
lo
g
3
x
,
g
(
x
)
=
log
3
(
81
x
)
g(x) = \log_3(81x)
g
(
x
)
=
lo
g
3
(
81
x
)
. Rewrite
g
g
g
with log properties and describe the transformation from
f
f
f
to
g
g
g
.
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7a.
Exponential, logarithmic, or linear? Explain.
x
x
x
: 5, 7, 11, 19;
y
y
y
: 1, 2, 3, 4
x
x
x
5
7
11
19
y
y
y
1
2
3
4
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7b.
Exponential, logarithmic, or linear? Explain.
x
x
x
: 1, 2, 3, 4;
y
y
y
: 1, 2, 4, 8
x
x
x
1
2
3
4
y
y
y
1
2
4
8
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7c.
Exponential, logarithmic, or linear? Explain.
x
x
x
: 2, 3, 4, 5;
log
y
\log y
lo
g
y
: 3, 7, 11, 15
x
x
x
2
3
4
5
log
y
\log y
lo
g
y
3
7
11
15
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8.
f
(
x
)
=
log
(
3
−
x
)
+
2
f(x) = \log(3-x) + 2
f
(
x
)
=
lo
g
(
3
−
x
)
+
2
. Find the asymptote, domain, range, end behavior, and sketch.
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9A(i).
(No calculator) Rewrite
g
(
x
)
=
log
2
(
x
3
)
+
log
4
x
g(x) = \log_2(x^3) + \log_4 x
g
(
x
)
=
lo
g
2
(
x
3
)
+
lo
g
4
x
as a single logarithm without negative exponents.
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9A(ii).
Rewrite
h
(
x
)
=
4
x
+
1
⋅
2
3
x
2
2
x
−
3
h(x) = \dfrac{4^{x+1}\cdot 2^{3x}}{2^{2x-3}}
h
(
x
)
=
2
2
x
−
3
4
x
+
1
⋅
2
3
x
as a single base with an exponent.
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9B.
k
(
x
)
=
5
+
6
log
4
x
k(x) = 5 + 6\log_4 x
k
(
x
)
=
5
+
6
lo
g
4
x
. Solve
k
(
x
)
=
17
k(x) = 17
k
(
x
)
=
17
.
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9C.
m
(
x
)
=
2
ln
x
−
ln
(
7
x
−
10
)
m(x) = 2\ln x - \ln(7x - 10)
m
(
x
)
=
2
ln
x
−
ln
(
7
x
−
10
)
. Find all inputs in the domain of
m
m
m
with output 0.
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10A(i).
f
f
f
is increasing for
x
>
0
x > 0
x
>
0
(table:
x
x
x
2, 4, 8, 16, 32 →
f
(
x
)
f(x)
f
(
x
)
8, 16, 24, 32, 40).
g
(
x
)
=
8.25
−
2
x
−
6
g(x) = 8.25 - 2^{x-6}
g
(
x
)
=
8.25
−
2
x
−
6
. Find
h
(
2
)
=
g
(
f
(
2
)
)
h(2) = g(f(2))
h
(
2
)
=
g
(
f
(
2
))
.
x
x
x
2
4
8
16
32
f
(
x
)
f(x)
f
(
x
)
8
16
24
32
40
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10A(ii).
Find
f
−
1
(
40
)
f^{-1}(40)
f
−
1
(
40
)
or say it's not defined.
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10B(i).
Find all
x
x
x
(decimals) with
g
(
x
)
=
4
g(x) = 4
g
(
x
)
=
4
, or say there are none.
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10B(ii).
End behavior of
g
g
g
as
x
x
x
decreases without bound (limit notation).
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10C(i).
Is
f
f
f
best modeled by a linear, quadratic, exponential, or logarithmic function?
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10C(ii).
Give a reason for C(i) using the change in inputs vs outputs from the table.
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