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Deck 6: Transformations of Functions and Their Graphs
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Question
Educational psychologists suggest that a child's intellectual capacity, I, can be represented as a function of time, t, in months, as follows:
,Where a > 0, b > 0 are constants. What is the effect on the graph of I of decreasing the value of b?
A) The graph gets closer to the asymptote more quickly.
B) The asymptote moves to the left.
C) The asymptote moves down.
D) The graph gets closer to the asymptote less quickly.
,Where a > 0, b > 0 are constants. What is the effect on the graph of I of decreasing the value of b?A) The graph gets closer to the asymptote more quickly.
B) The asymptote moves to the left.
C) The asymptote moves down.
D) The graph gets closer to the asymptote less quickly.
Question
Let 
. Which of the following formulas transforms the graph of g by shifting it 5 units to the right, reflecting it about the x-axis, and then shifting it up 3 units?
A)
B)
C)
D)
. Which of the following formulas transforms the graph of g by shifting it 5 units to the right, reflecting it about the x-axis, and then shifting it up 3 units?A)
B)
C)
D)
Question
Let 
. The domain of the formula that transforms the graph of g by shifting it 3 units to the right, reflecting it about the x-axis, and then shifting it up 6 units is all real numbers except x = _____.
. The domain of the formula that transforms the graph of g by shifting it 3 units to the right, reflecting it about the x-axis, and then shifting it up 6 units is all real numbers except x = _____. Question
Let 
. Let 
be the function that transforms the graph of g by shifting it 2 units to the right, reflecting it about the x-axis, and then shifting it up 7 units. Is 
even, odd, or neither?
. Let be the function that transforms the graph of g by shifting it 2 units to the right, reflecting it about the x-axis, and then shifting it up 7 units. Is even, odd, or neither? Question
A cup of coffee is initially at 150 
F, which is 75 
F above room temperature. The difference between the coffee's temperature and the room's temperature decreases at the hourly rate of 85%. Which of the following formulas gives T(t) , the coffee's temperature after t hours have elapsed?
A)
B)
C)
D)
F, which is 75 F above room temperature. The difference between the coffee's temperature and the room's temperature decreases at the hourly rate of 85%. Which of the following formulas gives T(t) , the coffee's temperature after t hours have elapsed?A)
B)
C)
D)
Question
Below is a graph of the function 
. If you were to sketch a graph of 
, what point would the point (4, 1) correspond to?
. If you were to sketch a graph of , what point would the point (4, 1) correspond to? Question
Below is a graph of the function 
. If you were to sketch a graph of 
, what point would the point (2, 0) correspond to?
. If you were to sketch a graph of , what point would the point (2, 0) correspond to? Question
Given the graph of 
below, find a possible formula fo 
r .
A)
B)
C)
D)
below, find a possible formula fo r .A)
B)
C)
D)
Question
One of these graphs shows a transformation of an exponential function, and one is a transformation of a log function. The remaining graph is not a transformation of either an exponential or log function. Which graph is the transformation of a log function?
A)
B)
C)
A)
B)
C)
Question
The graph of 
contains the point (-4, 0). What is the corresponding point on the graph of 
?
contains the point (-4, 0). What is the corresponding point on the graph of ? Question
The first figure is the graph of 
. Which of the other figures (a)-(f) show the graph of 
?
A)
B)
C)
D)
E)
F)
. Which of the other figures (a)-(f) show the graph of ?A)
B)
C)
D)
E)
F)
Question
The graph of 
is shown in the first figure. Which of the other graphs (a)-(d) correspond to the formula 
?
A)
B)
C)
D)
is shown in the first figure. Which of the other graphs (a)-(d) correspond to the formula ? A)
B)
C)
D)
Question
Let 
be the profit made by a water park in terms of the number of people, n, visiting the park each day. If 
people attended the park yesterday, what is meant by the expression 
?
A) 10 percent of yesterday's profit
B) Yesterday's profit if 10 times as many people had visited
C) Yesterday's profit plus an additional $10
D) Yesterday's profit if an additional 10 people had visited
be the profit made by a water park in terms of the number of people, n, visiting the park each day. If people attended the park yesterday, what is meant by the expression ?A) 10 percent of yesterday's profit
B) Yesterday's profit if 10 times as many people had visited
C) Yesterday's profit plus an additional $10
D) Yesterday's profit if an additional 10 people had visited
Question
The point (a, b) lies on the graph of 
. If the graph is reflected across the y-axis and compressed toward the y-axis by a factor of d (with d < 1), and then translated downward 3 units, what are the new coordinates for the point (a, b)?
A)
B)
C)
D)
. If the graph is reflected across the y-axis and compressed toward the y-axis by a factor of d (with d < 1), and then translated downward 3 units, what are the new coordinates for the point (a, b)?A)
B)
C)
D)
Question
Let 
. Which of the following describe how the function 
transforms the graph of f ?
A)
B)
C)
D)
. Which of the following describe how the function transforms the graph of f ?A)
B)
C)
D)
Question
Let 
. Which of the following describe how the function 
transforms the graph of f ?
A)
B)
C)
D)
. Which of the following describe how the function transforms the graph of f ?A)
B)
C)
D)
Question
Question
Question
Question
Question
Let 4 and -4 be the zeros of the quadratic function 
What are the zeros of the function
?
A) 4
B) -4
C) 2
D) -2
E) 8
F)-8
What are the zeros of the function?A) 4
B) -4
C) 2
D) -2
E) 8
F)-8
Question
Let 
be defined by the following graph, and let 
and 
.
Arrange the following values in order from least to greatest by placing a "1" next to the least, a "2" next to the next least, etc.
A.
B.
C.
be defined by the following graph, and let and . Arrange the following values in order from least to greatest by placing a "1" next to the least, a "2" next to the next least, etc.A.
B.
C.
Question
Use the table below to answer the following questions.
If 
, compute
A)
B)
C)
If , computeA)
B)
C)
Question
Sketch the graph of 
Question
The graph of 
contains the point (2, 3). What is the corresponding point on the graph of 
?
contains the point (2, 3). What is the corresponding point on the graph of ? Question
Given 
, the following figure shows the graphs of 
, 
, and 
. Which curve is the graph of 
?
, the following figure shows the graphs of , , and . Which curve is the graph of ? Question
Using the following table, find 
for x = -0.5. 
for x = -0.5. Question
Let 
be the height of a box in inches. Find a formula for the height 
in feet?
be the height of a box in inches. Find a formula for the height in feet?
Question
The graphs of f
and
are shown at the right. 
.
Which of the following gives a formula for
in terms of 
?
A)
B)
C)
D)
and
are shown at the right. . Which of the following gives a formula for
in terms of ?A)
B)
C)
D)
Question
Suppose 
is an even function. Determine whether 
is odd, even, or neither. Write "cannot tell" if there is not enough information to determine.
is an even function. Determine whether is odd, even, or neither. Write "cannot tell" if there is not enough information to determine. Question
Suppose 
is an odd function. Determine whether 
is odd, even, or neither. Write "cannot tell" if there is not enough information to determine.
is an odd function. Determine whether is odd, even, or neither. Write "cannot tell" if there is not enough information to determine. Question
Let 
represent the volume of a box with square base of side length 
and height 6. By what percent does the volume increase if the side length is increased by 20%?
represent the volume of a box with square base of side length and height 6. By what percent does the volume increase if the side length is increased by 20%? Question
Let 
represent the volume in cubic feet of a box with square base of side length 
Feet and height 8 feet. Let 
represent the volume in cubic inches of a box with square base of side length 
inches and height 96 inches. Which of the following is the correct formula for 
In terms of
?
A)
B)
C)
D)
represent the volume in cubic feet of a box with square base of side length Feet and height 8 feet. Let represent the volume in cubic inches of a box with square base of side length inches and height 96 inches. Which of the following is the correct formula for In terms of?A)
B)
C)
D)
Question
The domain of 
is 
and the range is 
. What is the domain and range of 
?
is and the range is . What is the domain and range of ? Question
Describe the effect of the transformation 
on the graph of 
on the graph of Question
Let 
be the value of an investment 
months after the account was open. Write an expression that represents the value of the investment increased by 15%.
be the value of an investment months after the account was open. Write an expression that represents the value of the investment increased by 15%. Question
Which of the following describes the effect of the transformation 
On the graph of the function 
?
A) The graph is stretched vertically by a factor of 6 and stretched horizontally by a factor of 6.
B) The graph is stretched vertically by a factor of 6 and shrunk horizontally by a factor of 1/8.
C) The graph is shrunk vertically by a factor of 1/8 and stretched horizontally by a factor of 6.
D) The graph is shrunk vertically by a factor of 1/8 and shrunk horizontally by a factor of 1/8 .
On the graph of the function ?A) The graph is stretched vertically by a factor of 6 and stretched horizontally by a factor of 6.
B) The graph is stretched vertically by a factor of 6 and shrunk horizontally by a factor of 1/8.
C) The graph is shrunk vertically by a factor of 1/8 and stretched horizontally by a factor of 6.
D) The graph is shrunk vertically by a factor of 1/8 and shrunk horizontally by a factor of 1/8 .
Question
Which of the following describes the effect of the transformation 
On the graph of the function 
?
A) The graph is stretched vertically by a factor of 4 and stretched horizontally by a factor of 4.
B) The graph is stretched vertically by a factor of 4 and compressed horizontally by a factor of 1/5 .
C) The graph is compressed vertically by a factor of 1/5 and stretched horizontally by a factor of 4.
D) The graph is compressed vertically by a factor of 1/5 and compressed horizontally by a factor of 1/5 .
On the graph of the function ?A) The graph is stretched vertically by a factor of 4 and stretched horizontally by a factor of 4.
B) The graph is stretched vertically by a factor of 4 and compressed horizontally by a factor of 1/5 .
C) The graph is compressed vertically by a factor of 1/5 and stretched horizontally by a factor of 4.
D) The graph is compressed vertically by a factor of 1/5 and compressed horizontally by a factor of 1/5 .
Question
The point 
lies on the graph of 
. What point must lie on the graph of 
?
lies on the graph of . What point must lie on the graph of ? Question
The point 
lies on the graph of 
. If the graph of 11ee8201_b9fd_2ffc_8e66_930a3c09055a_TB10073_11 is compressed vertically by a factor of 
and stretched horizontally by a factor of 9, what point must lie on the transformed graph?
lies on the graph of . If the graph of 11ee8201_b9fd_2ffc_8e66_930a3c09055a_TB10073_11 is compressed vertically by a factor of and stretched horizontally by a factor of 9, what point must lie on the transformed graph? Question
The point 
lies on the graph of 
. If the graph of f is stretched vertically by a factor of 9 and compressed horizontally by a factor of 
, what point must lie on the transformed graph?
lies on the graph of . If the graph of f is stretched vertically by a factor of 9 and compressed horizontally by a factor of , what point must lie on the transformed graph? Question
The point 
lies on the graph of 
. If the graph of f is compressed vertically by a factor of 5 and compressed horizontally by a factor of 
, what point must lie on the transformed graph?
lies on the graph of . If the graph of f is compressed vertically by a factor of 5 and compressed horizontally by a factor of , what point must lie on the transformed graph? Question
The following figure shows the graph of 
And the graphs of several multiples of 
.
Which of the following statements are true?
A) c < 0
B) c < d
C) d < 0
And the graphs of several multiples of . Which of the following statements are true?A) c < 0
B) c < d
C) d < 0
Question
Below is a graph of the function 
. If you were to sketch a graph of 
, what point would the point (0.6, -0.4) correspond to?
. If you were to sketch a graph of , what point would the point (0.6, -0.4) correspond to? Question
The following table gives values for 
, the cost per foot of drilling a well at a depth of x feet. The prices given are for wells drilled on a certain ranch in Texas.
Estimate the cost of drilling a well that is 40 feet deep.
, the cost per foot of drilling a well at a depth of x feet. The prices given are for wells drilled on a certain ranch in Texas. Estimate the cost of drilling a well that is 40 feet deep. Question
The following table gives values for 
, the cost per foot of drilling a well at a depth of x feet. The prices given are for wells drilled on a certain ranch in Texas. 
The ranch sits above a dense layer of bedrock. At what depth do you estimate that the bedrock layer begins?
A) Between 40 and 60 feet.
B) Between 100 and 120 feet.
C) Between 60 and 80 feet.
D) Between 80 and 100 feet.
, the cost per foot of drilling a well at a depth of x feet. The prices given are for wells drilled on a certain ranch in Texas. The ranch sits above a dense layer of bedrock. At what depth do you estimate that the bedrock layer begins?A) Between 40 and 60 feet.
B) Between 100 and 120 feet.
C) Between 60 and 80 feet.
D) Between 80 and 100 feet.
Question
Let 
. Write a formula for the following transformations of f.
A)
B)
C)
. Write a formula for the following transformations of f.A)
B)
C)
Question
The graph of 
is given below. Sketch a graph of 
is given below. Sketch a graph of Question
A bowling alley charges $3.10 for shoes plus $2.00 per game bowled. Let 
Be the total cost for bowling g games (including shoe rental). Now suppose the bowling alley decides to increase the cost for shoes by $1.10 and include the first game for free. What is the formula for the new total cost,
, of bowling g games as a transformation of 
?
A)
B)
C)
D)
Be the total cost for bowling g games (including shoe rental). Now suppose the bowling alley decides to increase the cost for shoes by $1.10 and include the first game for free. What is the formula for the new total cost,, of bowling g games as a transformation of ?A)
B)
C)
D)
Question
The amount of money in your bank account is given by 
. Which of the following formulas matches the description "$110 more than I have in my bank account"?
A)
B)
C)
D)
. Which of the following formulas matches the description "$110 more than I have in my bank account"?
A)
B)
C)
D)
Question
The amount of money in your bank account is given by 
. Which of the following formulas matches the description "the amount of money I will have in my bank account 30 years from now"?
A)
B)
C)
D)
. Which of the following formulas matches the description "the amount of money I will have in my bank account 30 years from now"?
A)
B)
C)
D)
Question
The domain of 
is 
and the range is 
. What is the domain and range of 
?
is and the range is . What is the domain and range of ? Question
The graph of 
is the graph of 
after it has been vertically stretched or shrunk. The point (5, 12) lies on the graph of 
. The corresponding point on the graph of
is 
. What is a possible formula for 
in terms of 
?
is the graph of after it has been vertically stretched or shrunk. The point (5, 12) lies on the graph of . The corresponding point on the graph of is . What is a possible formula for in terms of ? Question
The graphs of 
and
are shown below. 
.Which of the following gives a formula for
in terms of 
?
A)
B)
C)
D)
and are shown below. .Which of the following gives a formula for
in terms of ?A)
B)
C)
D)
Question
The graph of 
contains the point (3,-2). What corresponding point must be on the graph of 
?
contains the point (3,-2). What corresponding point must be on the graph of ? Question
The graph of 
Contains the point (4,-5). Which of the following points must be on the graph of 
?
A)
B)
C)
D)
Contains the point (4,-5). Which of the following points must be on the graph of ?A)
B)
C)
D)
Question
The function 
is obtained from 
by a single transformation. Use the tables below to find a formula for 
in terms of 
. 
is obtained from by a single transformation. Use the tables below to find a formula for in terms of . Question
If 
is an odd function, determine whether 
is odd, even, or neither. State "cannot tell" if there is not enough information to determine.
is an odd function, determine whether is odd, even, or neither. State "cannot tell" if there is not enough information to determine. Question
If 
is an even function, determine whether 
is odd, even, or neither. State "cannot tell" if there is not enough information to determine.
is an even function, determine whether is odd, even, or neither. State "cannot tell" if there is not enough information to determine. Question
The domain of 
is 
and the range is 
. If 
, what is the domain and range of 
?
is and the range is . If , what is the domain and range of ? Question
Suppose the range of 
is 
. Let 
. There exists some 
such that 
.
is . Let . There exists some such that . Question
Graph 
if 
.
if . Question
Graph 
if 
.
if . Question
The average rate of change of 
over 
is -4. Find the average rate of change of 
over 
.
over is -4. Find the average rate of change of over . Question
If the graph of the line 
is reflected about the x-axis, the resulting line has the equation y = _____ x + _____.
is reflected about the x-axis, the resulting line has the equation y = _____ x + _____. Question
Question
The function 
has odd symmetry and the function 
has even symmetry. Is the function 
odd, even, or neither?
has odd symmetry and the function has even symmetry. Is the function odd, even, or neither? Question
The function 
has odd symmetry and the function 
has even symmetry. Is the function 
odd, even, or neither?
has odd symmetry and the function has even symmetry. Is the function odd, even, or neither? Question
The function 
has odd symmetry and the function 
has even symmetry. Is the function 
odd, even, or neither?
has odd symmetry and the function has even symmetry. Is the function odd, even, or neither? Question
Some of the values of 
are given in the following table. If 
is an even function, what is 
?
are given in the following table. If is an even function, what is ? Question
The following table gives values for the functions f and g.
Which of the following statements are true?
A) f is symmetric about the x-axis.
B) g is symmetric about the x-axis.
C) f is symmetric about the y-axis.
D) g is symmetric about the y-axis.
E) f is symmetric about the origin.
F)g is symmetric about the origin.
Which of the following statements are true?A) f is symmetric about the x-axis.
B) g is symmetric about the x-axis.
C) f is symmetric about the y-axis.
D) g is symmetric about the y-axis.
E) f is symmetric about the origin.
F)g is symmetric about the origin.
Question
The following table gives some values for the function 
. If 
has even symmetry, what is 
?
. If has even symmetry, what is ? Question
The graph of 
contains the point (2, -3). What point must lie on the reflected graph if the graph is reflected about the x-axis?
contains the point (2, -3). What point must lie on the reflected graph if the graph is reflected about the x-axis? Question
The graph of 
contains the point (2, -1). What is the corresponding point on the graph if 
is an odd function?
contains the point (2, -1). What is the corresponding point on the graph if is an odd function? Question
Given the following table of values for 
, find 
when x = 2. If you do not have sufficient information, enter "cannot determine". 
, find when x = 2. If you do not have sufficient information, enter "cannot determine". Question
How are the graphs of 
And 
related?
A)
B)
C)
D)
E) None of the above.
And related?A)
B)
C)
D)
E) None of the above.
Question
What is the formula for 
if
?
A)
B)
C)
D)
if ?A)
B)
C)
D)
Question
Is the function 
odd, even, or neither?
odd, even, or neither? Question
If the following is the graph of 
. 
Sketch the graph of
.
. Sketch the graph of
. Question
The following is the graph of 
. 
Sketch the graph of 
.
. Sketch the graph of .
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Deck 6: Transformations of Functions and Their Graphs
1
Educational psychologists suggest that a child's intellectual capacity, I, can be represented as a function of time, t, in months, as follows:
,Where a > 0, b > 0 are constants. What is the effect on the graph of I of decreasing the value of b?
A) The graph gets closer to the asymptote more quickly.
B) The asymptote moves to the left.
C) The asymptote moves down.
D) The graph gets closer to the asymptote less quickly.
,Where a > 0, b > 0 are constants. What is the effect on the graph of I of decreasing the value of b?A) The graph gets closer to the asymptote more quickly.
B) The asymptote moves to the left.
C) The asymptote moves down.
D) The graph gets closer to the asymptote less quickly.
The graph gets closer to the asymptote less quickly.
2
Let . Which of the following formulas transforms the graph of g by shifting it 5 units to the right, reflecting it about the x-axis, and then shifting it up 3 units?
A)
B)
C)
D)
. Which of the following formulas transforms the graph of g by shifting it 5 units to the right, reflecting it about the x-axis, and then shifting it up 3 units?A)
B)
C)
D)
3
Let . The domain of the formula that transforms the graph of g by shifting it 3 units to the right, reflecting it about the x-axis, and then shifting it up 6 units is all real numbers except x = _____.
. The domain of the formula that transforms the graph of g by shifting it 3 units to the right, reflecting it about the x-axis, and then shifting it up 6 units is all real numbers except x = _____.3
4
Let . Let be the function that transforms the graph of g by shifting it 2 units to the right, reflecting it about the x-axis, and then shifting it up 7 units. Is even, odd, or neither?
. Let be the function that transforms the graph of g by shifting it 2 units to the right, reflecting it about the x-axis, and then shifting it up 7 units. Is even, odd, or neither? Unlock Deck
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5
A cup of coffee is initially at 150 F, which is 75 F above room temperature. The difference between the coffee's temperature and the room's temperature decreases at the hourly rate of 85%. Which of the following formulas gives T(t) , the coffee's temperature after t hours have elapsed?
A)
B)
C)
D)
F, which is 75 F above room temperature. The difference between the coffee's temperature and the room's temperature decreases at the hourly rate of 85%. Which of the following formulas gives T(t) , the coffee's temperature after t hours have elapsed?A)
B)
C)
D)
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6
Below is a graph of the function . If you were to sketch a graph of , what point would the point (4, 1) correspond to?
. If you were to sketch a graph of , what point would the point (4, 1) correspond to? Unlock Deck
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7
Below is a graph of the function . If you were to sketch a graph of , what point would the point (2, 0) correspond to?
. If you were to sketch a graph of , what point would the point (2, 0) correspond to? Unlock Deck
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8
Given the graph of below, find a possible formula fo r .
A)
B)
C)
D)
below, find a possible formula fo r .A)
B)
C)
D)
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9
One of these graphs shows a transformation of an exponential function, and one is a transformation of a log function. The remaining graph is not a transformation of either an exponential or log function. Which graph is the transformation of a log function?
A)
B)
C)
A)
B)
C)
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10
The graph of contains the point (-4, 0). What is the corresponding point on the graph of ?
contains the point (-4, 0). What is the corresponding point on the graph of ? Unlock Deck
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11
The first figure is the graph of . Which of the other figures (a)-(f) show the graph of ?
A)
B)
C)
D)
E)
F)
. Which of the other figures (a)-(f) show the graph of ?A)
B)
C)
D)
E)
F)
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12
The graph of is shown in the first figure. Which of the other graphs (a)-(d) correspond to the formula ?
A)
B)
C)
D)
is shown in the first figure. Which of the other graphs (a)-(d) correspond to the formula ? A)
B)
C)
D)
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13
Let be the profit made by a water park in terms of the number of people, n, visiting the park each day. If people attended the park yesterday, what is meant by the expression ?
A) 10 percent of yesterday's profit
B) Yesterday's profit if 10 times as many people had visited
C) Yesterday's profit plus an additional $10
D) Yesterday's profit if an additional 10 people had visited
be the profit made by a water park in terms of the number of people, n, visiting the park each day. If people attended the park yesterday, what is meant by the expression ?A) 10 percent of yesterday's profit
B) Yesterday's profit if 10 times as many people had visited
C) Yesterday's profit plus an additional $10
D) Yesterday's profit if an additional 10 people had visited
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14
The point (a, b) lies on the graph of . If the graph is reflected across the y-axis and compressed toward the y-axis by a factor of d (with d < 1), and then translated downward 3 units, what are the new coordinates for the point (a, b)?
A)
B)
C)
D)
. If the graph is reflected across the y-axis and compressed toward the y-axis by a factor of d (with d < 1), and then translated downward 3 units, what are the new coordinates for the point (a, b)?A)
B)
C)
D)
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15
Let . Which of the following describe how the function transforms the graph of f ?
A)
B)
C)
D)
. Which of the following describe how the function transforms the graph of f ?A)
B)
C)
D)
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16
Let . Which of the following describe how the function transforms the graph of f ?
A)
B)
C)
D)
. Which of the following describe how the function transforms the graph of f ?A)
B)
C)
D)
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17
The graph of a function f has been shifted down 4 units, shifted 4 units to the right, and then stretched vertically by a factor of 9. The new graph is produced by a function g. Find a formula for g in terms of f.
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18
The graph of a function f has been shifted down 2 units, shifted 5 units to the right, and then stretched vertically by a factor of 8, and compressed horizontally by a factor of 4. The new graph is produced by a function g. Find a formula for g in terms of f.
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19
The graph of a function f has been stretched vertically by a factor of 9, compressed horizontally by a factor of 6, and then shifted up 3 units and shifted 4 units to the left. The new graph is produced by a function g. Find a formula for g in terms of f.
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20
The point (2,4) lies on the graph of the function f. Suppose the graph of f is reflected across the y-axis, shifted upward 7 units, stretched vertically by a factor of 2, compressed horizontally by a factor of 16, and then shifted 6 units to the right. What point must lie on the transformed graph?
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21
Let 4 and -4 be the zeros of the quadratic function What are the zeros of the function
?
A) 4
B) -4
C) 2
D) -2
E) 8
F)-8
What are the zeros of the function?A) 4
B) -4
C) 2
D) -2
E) 8
F)-8
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22
Let be defined by the following graph, and let and .
Arrange the following values in order from least to greatest by placing a "1" next to the least, a "2" next to the next least, etc.
A.
B.
C.
be defined by the following graph, and let and . Arrange the following values in order from least to greatest by placing a "1" next to the least, a "2" next to the next least, etc.A.
B.
C.
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23
Use the table below to answer the following questions.
If , compute
A)
B)
C)
If , computeA)
B)
C)
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24
Sketch the graph of
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25
The graph of contains the point (2, 3). What is the corresponding point on the graph of ?
contains the point (2, 3). What is the corresponding point on the graph of ? Unlock Deck
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26
Given , the following figure shows the graphs of , , and . Which curve is the graph of ?
, the following figure shows the graphs of , , and . Which curve is the graph of ? Unlock Deck
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27
Using the following table, find for x = -0.5.
for x = -0.5. Unlock Deck
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28
Let be the height of a box in inches. Find a formula for the height
in feet?
be the height of a box in inches. Find a formula for the height in feet?
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29
The graphs of f
and are shown at the right. .
Which of the following gives a formula for in terms of ?
A)
B)
C)
D)
and
are shown at the right. . Which of the following gives a formula for
in terms of ?A)
B)
C)
D)
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30
Suppose is an even function. Determine whether is odd, even, or neither. Write "cannot tell" if there is not enough information to determine.
is an even function. Determine whether is odd, even, or neither. Write "cannot tell" if there is not enough information to determine. Unlock Deck
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31
Suppose is an odd function. Determine whether is odd, even, or neither. Write "cannot tell" if there is not enough information to determine.
is an odd function. Determine whether is odd, even, or neither. Write "cannot tell" if there is not enough information to determine. Unlock Deck
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32
Let represent the volume of a box with square base of side length and height 6. By what percent does the volume increase if the side length is increased by 20%?
represent the volume of a box with square base of side length and height 6. By what percent does the volume increase if the side length is increased by 20%? Unlock Deck
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33
Let represent the volume in cubic feet of a box with square base of side length Feet and height 8 feet. Let represent the volume in cubic inches of a box with square base of side length inches and height 96 inches. Which of the following is the correct formula for In terms of
?
A)
B)
C)
D)
represent the volume in cubic feet of a box with square base of side length Feet and height 8 feet. Let represent the volume in cubic inches of a box with square base of side length inches and height 96 inches. Which of the following is the correct formula for In terms of?A)
B)
C)
D)
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34
The domain of is and the range is . What is the domain and range of ?
is and the range is . What is the domain and range of ? Unlock Deck
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35
Describe the effect of the transformation on the graph of
on the graph of Unlock Deck
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36
Let be the value of an investment months after the account was open. Write an expression that represents the value of the investment increased by 15%.
be the value of an investment months after the account was open. Write an expression that represents the value of the investment increased by 15%. Unlock Deck
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37
Which of the following describes the effect of the transformation On the graph of the function ?
A) The graph is stretched vertically by a factor of 6 and stretched horizontally by a factor of 6.
B) The graph is stretched vertically by a factor of 6 and shrunk horizontally by a factor of 1/8.
C) The graph is shrunk vertically by a factor of 1/8 and stretched horizontally by a factor of 6.
D) The graph is shrunk vertically by a factor of 1/8 and shrunk horizontally by a factor of 1/8 .
On the graph of the function ?A) The graph is stretched vertically by a factor of 6 and stretched horizontally by a factor of 6.
B) The graph is stretched vertically by a factor of 6 and shrunk horizontally by a factor of 1/8.
C) The graph is shrunk vertically by a factor of 1/8 and stretched horizontally by a factor of 6.
D) The graph is shrunk vertically by a factor of 1/8 and shrunk horizontally by a factor of 1/8 .
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38
Which of the following describes the effect of the transformation On the graph of the function ?
A) The graph is stretched vertically by a factor of 4 and stretched horizontally by a factor of 4.
B) The graph is stretched vertically by a factor of 4 and compressed horizontally by a factor of 1/5 .
C) The graph is compressed vertically by a factor of 1/5 and stretched horizontally by a factor of 4.
D) The graph is compressed vertically by a factor of 1/5 and compressed horizontally by a factor of 1/5 .
On the graph of the function ?A) The graph is stretched vertically by a factor of 4 and stretched horizontally by a factor of 4.
B) The graph is stretched vertically by a factor of 4 and compressed horizontally by a factor of 1/5 .
C) The graph is compressed vertically by a factor of 1/5 and stretched horizontally by a factor of 4.
D) The graph is compressed vertically by a factor of 1/5 and compressed horizontally by a factor of 1/5 .
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39
The point lies on the graph of . What point must lie on the graph of ?
lies on the graph of . What point must lie on the graph of ? Unlock Deck
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40
The point lies on the graph of . If the graph of 11ee8201_b9fd_2ffc_8e66_930a3c09055a_TB10073_11 is compressed vertically by a factor of and stretched horizontally by a factor of 9, what point must lie on the transformed graph?
lies on the graph of . If the graph of 11ee8201_b9fd_2ffc_8e66_930a3c09055a_TB10073_11 is compressed vertically by a factor of and stretched horizontally by a factor of 9, what point must lie on the transformed graph? Unlock Deck
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41
The point lies on the graph of . If the graph of f is stretched vertically by a factor of 9 and compressed horizontally by a factor of , what point must lie on the transformed graph?
lies on the graph of . If the graph of f is stretched vertically by a factor of 9 and compressed horizontally by a factor of , what point must lie on the transformed graph? Unlock Deck
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42
The point lies on the graph of . If the graph of f is compressed vertically by a factor of 5 and compressed horizontally by a factor of , what point must lie on the transformed graph?
lies on the graph of . If the graph of f is compressed vertically by a factor of 5 and compressed horizontally by a factor of , what point must lie on the transformed graph? Unlock Deck
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43
The following figure shows the graph of And the graphs of several multiples of .
Which of the following statements are true?
A) c < 0
B) c < d
C) d < 0
And the graphs of several multiples of . Which of the following statements are true?A) c < 0
B) c < d
C) d < 0
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44
Below is a graph of the function . If you were to sketch a graph of , what point would the point (0.6, -0.4) correspond to?
. If you were to sketch a graph of , what point would the point (0.6, -0.4) correspond to? Unlock Deck
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45
The following table gives values for , the cost per foot of drilling a well at a depth of x feet. The prices given are for wells drilled on a certain ranch in Texas.
Estimate the cost of drilling a well that is 40 feet deep.
, the cost per foot of drilling a well at a depth of x feet. The prices given are for wells drilled on a certain ranch in Texas. Estimate the cost of drilling a well that is 40 feet deep. Unlock Deck
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46
The following table gives values for , the cost per foot of drilling a well at a depth of x feet. The prices given are for wells drilled on a certain ranch in Texas. The ranch sits above a dense layer of bedrock. At what depth do you estimate that the bedrock layer begins?
A) Between 40 and 60 feet.
B) Between 100 and 120 feet.
C) Between 60 and 80 feet.
D) Between 80 and 100 feet.
, the cost per foot of drilling a well at a depth of x feet. The prices given are for wells drilled on a certain ranch in Texas. The ranch sits above a dense layer of bedrock. At what depth do you estimate that the bedrock layer begins?A) Between 40 and 60 feet.
B) Between 100 and 120 feet.
C) Between 60 and 80 feet.
D) Between 80 and 100 feet.
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47
Let . Write a formula for the following transformations of f.
A)
B)
C)
. Write a formula for the following transformations of f.A)
B)
C)
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48
The graph of is given below. Sketch a graph of
is given below. Sketch a graph of Unlock Deck
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49
A bowling alley charges $3.10 for shoes plus $2.00 per game bowled. Let Be the total cost for bowling g games (including shoe rental). Now suppose the bowling alley decides to increase the cost for shoes by $1.10 and include the first game for free. What is the formula for the new total cost,
, of bowling g games as a transformation of ?
A)
B)
C)
D)
Be the total cost for bowling g games (including shoe rental). Now suppose the bowling alley decides to increase the cost for shoes by $1.10 and include the first game for free. What is the formula for the new total cost,, of bowling g games as a transformation of ?A)
B)
C)
D)
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50
The amount of money in your bank account is given by
. Which of the following formulas matches the description "$110 more than I have in my bank account"?
A)
B)
C)
D)
. Which of the following formulas matches the description "$110 more than I have in my bank account"?
A)
B)
C)
D)
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51
The amount of money in your bank account is given by
. Which of the following formulas matches the description "the amount of money I will have in my bank account 30 years from now"?
A)
B)
C)
D)
. Which of the following formulas matches the description "the amount of money I will have in my bank account 30 years from now"?
A)
B)
C)
D)
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52
The domain of is and the range is . What is the domain and range of ?
is and the range is . What is the domain and range of ? Unlock Deck
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53
The graph of is the graph of after it has been vertically stretched or shrunk. The point (5, 12) lies on the graph of . The corresponding point on the graph of
is . What is a possible formula for in terms of ?
is the graph of after it has been vertically stretched or shrunk. The point (5, 12) lies on the graph of . The corresponding point on the graph of is . What is a possible formula for in terms of ? Unlock Deck
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54
The graphs of and are shown below.
.Which of the following gives a formula for in terms of ?
A)
B)
C)
D)
and are shown below. .Which of the following gives a formula for
in terms of ?A)
B)
C)
D)
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55
The graph of contains the point (3,-2). What corresponding point must be on the graph of ?
contains the point (3,-2). What corresponding point must be on the graph of ? Unlock Deck
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56
The graph of Contains the point (4,-5). Which of the following points must be on the graph of ?
A)
B)
C)
D)
Contains the point (4,-5). Which of the following points must be on the graph of ?A)
B)
C)
D)
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57
The function is obtained from by a single transformation. Use the tables below to find a formula for in terms of .
is obtained from by a single transformation. Use the tables below to find a formula for in terms of . Unlock Deck
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58
If is an odd function, determine whether is odd, even, or neither. State "cannot tell" if there is not enough information to determine.
is an odd function, determine whether is odd, even, or neither. State "cannot tell" if there is not enough information to determine. Unlock Deck
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59
If is an even function, determine whether is odd, even, or neither. State "cannot tell" if there is not enough information to determine.
is an even function, determine whether is odd, even, or neither. State "cannot tell" if there is not enough information to determine. Unlock Deck
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60
The domain of is and the range is . If , what is the domain and range of ?
is and the range is . If , what is the domain and range of ? Unlock Deck
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61
Suppose the range of is . Let . There exists some such that .
is . Let . There exists some such that . Unlock Deck
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62
Graph if .
if . Unlock Deck
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63
Graph if .
if . Unlock Deck
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64
The average rate of change of over is -4. Find the average rate of change of over .
over is -4. Find the average rate of change of over . Unlock Deck
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65
If the graph of the line is reflected about the x-axis, the resulting line has the equation y = _____ x + _____.
is reflected about the x-axis, the resulting line has the equation y = _____ x + _____. Unlock Deck
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66
An even function is decreasing and concave down in the first quadrant. How does the function behave in the second quadrant?
A) It is decreasing and concave down
B) It is increasing and concave up
C) It is increasing and concave down
D) It is decreasing and concave up
A) It is decreasing and concave down
B) It is increasing and concave up
C) It is increasing and concave down
D) It is decreasing and concave up
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67
The function has odd symmetry and the function has even symmetry. Is the function odd, even, or neither?
has odd symmetry and the function has even symmetry. Is the function odd, even, or neither? Unlock Deck
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68
The function has odd symmetry and the function has even symmetry. Is the function odd, even, or neither?
has odd symmetry and the function has even symmetry. Is the function odd, even, or neither? Unlock Deck
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69
The function has odd symmetry and the function has even symmetry. Is the function odd, even, or neither?
has odd symmetry and the function has even symmetry. Is the function odd, even, or neither? Unlock Deck
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70
Some of the values of are given in the following table. If is an even function, what is ?
are given in the following table. If is an even function, what is ? Unlock Deck
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71
The following table gives values for the functions f and g.
Which of the following statements are true?
A) f is symmetric about the x-axis.
B) g is symmetric about the x-axis.
C) f is symmetric about the y-axis.
D) g is symmetric about the y-axis.
E) f is symmetric about the origin.
F)g is symmetric about the origin.
Which of the following statements are true?A) f is symmetric about the x-axis.
B) g is symmetric about the x-axis.
C) f is symmetric about the y-axis.
D) g is symmetric about the y-axis.
E) f is symmetric about the origin.
F)g is symmetric about the origin.
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72
The following table gives some values for the function . If has even symmetry, what is ?
. If has even symmetry, what is ? Unlock Deck
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73
The graph of contains the point (2, -3). What point must lie on the reflected graph if the graph is reflected about the x-axis?
contains the point (2, -3). What point must lie on the reflected graph if the graph is reflected about the x-axis? Unlock Deck
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74
The graph of contains the point (2, -1). What is the corresponding point on the graph if is an odd function?
contains the point (2, -1). What is the corresponding point on the graph if is an odd function? Unlock Deck
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75
Given the following table of values for , find when x = 2. If you do not have sufficient information, enter "cannot determine".
, find when x = 2. If you do not have sufficient information, enter "cannot determine". Unlock Deck
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76
How are the graphs of And related?
A)
B)
C)
D)
E) None of the above.
And related?A)
B)
C)
D)
E) None of the above.
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77
What is the formula for if ?
A)
B)
C)
D)
if ?A)
B)
C)
D)
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78
Is the function odd, even, or neither?
odd, even, or neither? Unlock Deck
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79
If the following is the graph of .
Sketch the graph of .
. Sketch the graph of
. Unlock Deck
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80
The following is the graph of . Sketch the graph of .
. Sketch the graph of . Unlock Deck
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