Download Sketch and analyze the graph of each function.

D = (– , ); R = (–
asymptote: x-axis;
, 0); y-intercept: –e ;
decreasing for (–
Practice Test - Chapter 3
,
Sketch and analyze the graph of each function.
Describe its domain, range, intercepts,
asymptotes, end behavior, and where the
function is increasing or decreasing.
)
Use the graph of f (x) to describe the
transformation that results in the graph of g(x).
Then sketch the graphs of f (x) and g(x).
3. 1. f (x) = –ex + 7
;
SOLUTION: SOLUTION: Evaluate the function for several x-values in its
domain.
x
−7
−5 −4
−3
y
−1 −7.4 −20.1 −54.6
Then use a smooth curve to connect each of these
ordered pairs.
This function is of the form
. Therefore,
the graph of g(x) is the graph of f (x) translated 3
units to the right and 4 units up. The translation to the
right is indicated by the subtraction of 3 in the
exponent. The translation up is indicated by the
addition of 4.
Use the graphs of the functions to confirm this
transformation.
List the domain, range, intercepts, asymptotes, end
behavior, and where the function is increasing or
decreasing.
7
D = (– , ); R = (– , 0); y-intercept: –e ;
asymptote: x-axis;
decreasing for (–
,
)
5. MULTIPLE CHOICE For which function is Use the graph of f (x) to describe the
transformation that results in the graph of g(x).
Then sketch the graphs of f (x) and g(x).
3. −x
A f (x) = –2 · 3
B
;
C f (x) = –log8 (x – 5)
SOLUTION: D f (x) = log3 (–x) – 6
This function is of the form
. Therefore,
the graph of g(x) is the graph of f (x) translated 3
units to the right and 4 units up. The translation to the
right is indicated by the subtraction of 3 in the
exponent. The translation up is indicated by the
addition of 4.
Use the graphs of the functions to confirm this
transformation.
SOLUTION: −x
For option A, as x approaches infinity, 3
approaches 0, so the function approaches 0. For
option B, as x approaches infinity,
approaches
0, so the function approaches 0. For option D, as x
approaches infinity, log3 (−x) is undefined. For option
C, as x approaches infinity, log8 (x − 5) approaches
infinity and − log8 (x − 5) approaches negative
infinity. The correct choice is C.
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Evaluate each expression.
7. log32 2
9. SOLUTION: Practice Test - Chapter 3
5. MULTIPLE CHOICE For which function is Sketch the graph of each function.
11. g(x) = log (–x) + 5
−x
A f (x) = –2 · 3
SOLUTION: B
Evaluate the function for several x-values in its
domain.
C f (x) = –log8 (x – 5)
D f (x) = log3 (–x) – 6
SOLUTION: −x
For option A, as x approaches infinity, 3
approaches 0, so the function approaches 0. For
option B, as x approaches infinity,
x −3
0
−2 −1
y 5.48
5.30 5
undef.
Then use a smooth curve to connect each of these
ordered pairs.
approaches
0, so the function approaches 0. For option D, as x
approaches infinity, log3 (−x) is undefined. For option
C, as x approaches infinity, log8 (x − 5) approaches
infinity and − log8 (x − 5) approaches negative
infinity. The correct choice is C.
Evaluate each expression.
7. log32 2
SOLUTION: Expand each expression.
13. log6 36xy2
SOLUTION: 15. GEOLOGY Richter scale magnitude of an
earthquake can be calculated using
where E is the energy produced
and E0 is a constant.
9. SOLUTION: Sketch the graph of each function.
11. g(x) = log (–x) + 5
a. An earthquake with a magnitude of 7.1 hit San
Francisco in 1989. Find the scale of an earthquake
that produces 10 times the energy of the 1989
earthquake.
b. In 1906, San Francisco had an earthquake
registering 8.25. How many times as much energy
did the 1906 earthquake produce as the 1989
earthquake?
SOLUTION: SOLUTION: Evaluate the function for several x-values in its
domain.
a. If E is the energy produced by the 1989
earthquake, then 10 times this energy is 10E. Use
the 1989 data to solve for E0, then replace E with
10E to find the magnitude of an earthquake with 10
Page 2
times the energy.
x
−3
−2
−1
0
eSolutions
y Manual
5.48 - Powered
5.30 5by Cognero
undef.
Then use a smooth curve to connect each of these
SOLUTION: a. If E is the energy produced by the 1989
earthquake, then 10 times this energy is 10E. Use
Practice
Test
- Chapter
the 1989
data to
solve for E03
, then replace E with
10E to find the magnitude of an earthquake with 10
times the energy.
The magnitude is about 7.8.
b. For this problem, we need to find the energy of
the 1906 earthquake in relation to the 1989
earthquake E. Let the 1906 earthquake = nE.
Now, solve for R.
The 1906 earthquake produced about 53 times as
much energy as the 1989 earthquake.
Condense each expression.
17. 1 + ln 3 – 4 ln x
SOLUTION: The magnitude is about 7.8.
b. For this problem, we need to find the energy of
the 1906 earthquake in relation to the 1989
earthquake E. Let the 1906 earthquake = nE.
Solve each equation.
19. e2x – 3ex + 2 = 0
SOLUTION: x = ln 2 or 0
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21. log2 (x – 1) + 1 = log2 (x + 3)
SOLUTION: Page 3
Practice
x = ln 2Test
or 0 - Chapter 3
25. CENSUS The table gives the U.S. population
between 1790 and 1940. Let 1780 = 0.
21. log2 (x – 1) + 1 = log2 (x + 3)
SOLUTION: For Exercises 23 and 24, complete each step.
a. Find an exponential or logarithmic function to
model the data.
b. Find the value of each model at x = 20.
a. Linearize the data, assuming a quadratic model.
Graph the data and write an equation for a line of
best fit.
b. Use the linear model to find a model for the
original data. Is a quadratic model a good
representation of population growth? Explain.
SOLUTION: 23. SOLUTION: a. An exponential regression cannot be completed
with negative y-values. Calculate the logarithmic
regression.
The rounded logarithmic regression equation is f (x) =
8.20 – 5.11ln x.
b. Using the full regression equation, f (20) ≈ −7.11.
a. What linearizing data according to a quadratic
model, use (x,
).
Plot the data.
Find the regression.
25. CENSUS The table gives the U.S. population
between 1790 and 1940. Let 1780 = 0.
The rounded regression equation is y = 0.07x.
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b. Substitute
for and solve for y.
Page 4
Practice
Test - Chapter 3
The rounded regression equation is y = 0.07x.
b. Substitute
for and solve for y.
2
The rounded regression equation is y = 0.0041x +
0.1331x + 1.0816. Population growth generally does
not grow without bounds. Typically, it will start to
level off and plateau. For these reasons, a logistic
model would be more appropriate.
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