Download Reading 4.7

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LESSON
4-7
Reading Strategies
Read a Table
Exponential and logarithmic functions as well as linear, quadratic, and
polynomial functions can all undergo the same types of transformations.
Parent function: f (x)
Vertical translation
f (x ) + k
k > 0 up
k < 0 down
Horizontal translation
f (x − h)
h > 0 right
h < 0 left
Reflection
Vertical stretch or compression
−f (x)
across x-axis
f (−x)
across y-axis
af (x)
a > 1 stretch
0 < a < 1 compression
Horizontal stretch or compression
⎛1 ⎞
f ⎜ x⎟
⎝b ⎠
b > 1 stretch
0 < b < 1 compression
Use the chart to answer the questions below.
1. How does the graph of f (x) = ln x compare to the graph of g(x) = ln x − 4?
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2. How does the graph of f (x) = ex compare to the graph of g(x) = e(x − 5)?
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3. Describe the transformation of g(x) = 8 ex from the parent function.
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4. How does the graph of g(x) = −ln x compare to the graph of f (x) = ln x?
_________________________________________________________________________________________
5. Write the transformed function, g(x), if
f (x) = ln x is translated 7 units left.
6. Write the transformed function, g(x), if
f (x) = ex is reflected over the y-axis.
7. Write the transformed function, g(x), if f (x) = log x
1
is horizontally compressed by a factor of .
6
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Holt McDougal Algebra 2
3. g(x) = −7 ⋅ 9x − 1
4. x = 1
⎛2
⎞
4. g(x)= −3ln ⎜ x + 8 ⎟ + 7
⎝3
⎠
5. f(x)= −log(3x + 11) − 2
6. f(x) = −4 ⋅ 7x − 1 + 5
7. Translate 2 units up and 2 units right
and then reflect across the x-axis
8. $27,647.16
Reteach
Challenge
1. 3
1. They are identical. The graphs are
reflections of f(x) = log x over the x-axis.
1
2. log = log x −1 = −1 x log x = − log x
x
3. They are identical. The function is
vertically compressed by a factor of 0.5
and then translated 2 units up.
( )
(
)
4. log 100 x = log100 + log x
1
= log 102 + log x 2 = 2log10 +
2. 4; y = 0
1
log x
log x = 2 +
2
2
5. The three functions are identical. The
function is horizontally compressed by
a factor of 2 and then shifted 1.5 units
right.
4x
4x
2 x − 1.5 )
6. 22 x − 3 = 2 (
= 4 x − 1.5 = 1.5 =
8
4
Problem Solving
1. a. About 3 ft tall
b. About 0.45 ft; that is the initial height
of the plant.
2. a. g(t) = ln t
3. x = 0
b. The parent function is translated 1.25
units left and stretched vertically by a
factor of 2.
c. B
3. A
4. H
Reading Strategies
1. Possible answer: The shapes of the
curves are the same, but the curve for
g(x) is shifted 4 units down from the
curve for f(x).
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A51
Holt McDougal Algebra 2
2. Possible answer: The shapes of the
curves are the same, but the curve for
g(x) is shifted 5 units right of the curve
for f(x).
3. Possible answer: The curve for g(x) is a
vertical stretch of the parent
function by a factor of 8.
4. Possible answer: The curve for g(x) is
the curve for f(x) reflected across
the x-axis.
5. g(x) = ln (x + 7)
6. g(x) = e−x
7. g(x) = log 6x
3. Yes;
3
2
2
3
5. f(x) = 4(2.3)x
6. f(x) = 3035(0.35)x
7. f(x) = −4 + 0.5 ln x
8. f(x) = 1.97 − 0.7 ln x
9. a. 350(1.18)x
b. 11.9 min
c. 7,194,299
Reteach
4-8 CURVE FITTING WITH
1. 18, 72
Practice A
2. 8, 24, 72, 216
4.5
18
72
= 4,
= 4,
= 4; data set is
1.125
4.5
18
exponential with a constant ratio of 4.
EXPONENTIAL AND LOGARITHMIC
MODELS
1. a. 0.25, 1, 4,16, 64
64
16
4
1
= 4,
= 4, = 4,
=4
b.
16
4
1
0.25
24
72
216
= 3,
= 3,
= 3; data set is
8
24
72
exponential with a constant ratio of 3.
c. Yes, 4
3. a. B(t) ≈ 251.9(1.4)t
d. Yes
2. Yes; 5
b. About 5.8 min
3. No
Challenge
4. a. a = 24, b = 0.5
1. Independent variable, years; dependent
variable, number of subscribers;
exponential model
b. f(x) = 24(0.5x)
5. a. a = 3.3, b = 2
b. f(x) = 3.2(2x)
2. y ≈ 0.67(1.39)x; yes, because r2 =
0.9767
Practice B
1. No
3. Predicted value is about 67,341,000,
which is close to the estimated number.
2. Yes; 6
3. Yes; 3
4. No
x
5. f(x) = 29(0.49)
3.8(1.15)x
4. Possible answer: Predicted value is
about 130,110,000, which is slightly
higher than the estimated number.
6. f(x) =
7. a. f(x) = 0.97(1.16)x
5. Possible answer: Predicted value is
485,703,000, which is more than twice
the estimated number.
b. 15 cm
c. $367.36
8. a. f(x) = 1.14 + 8.42 ln x
6. Looking at the curve, as you move to
the right, the graph of the model rises
very sharply and grossly overestimates
the number of subscribers.
b. 9.4 s
c. 35.6 m/s
Practice C
1. Yes; 1.25
4. Yes;
Problem Solving
2. No
1. a. W(t) = 47.34(1.13)t
b. 2016
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