Deck 1: Preparation for Calculus
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Deck 1: Preparation for Calculus
1
Match the graph of the function given below with the graph of its inverse function.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)



2
Write the following expression as a logarithm of a single quantity.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)


3
Solve the following equation for x.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)


4
What is the domain of the function
?
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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5
What is the domain of the function
?
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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6
Solve the following equation for x.
A)
B)
C)
D)
E)no solution

A)

B)

C)

D)

E)no solution
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7
Find
if
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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8
Find
if
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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9
Find
if
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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10
Solve the following equation for x.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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11
Find
if
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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k this deck
12
Use the Horizontal Line Test to determine whether the following statement is true or false.
The function
is one-to-one on its entire domain and therefore has an inverse function.
The function

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13
Solve the following equation for x.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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14
True or False: The function
is one-to-one on the domain
.


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15
Write the following expression as a logarithm of a single quantity.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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16
Find
if
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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17
Find
if
.
A)
B)
C)
D)
E)
does not exist


A)

B)

C)

D)

E)

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18
Use the Horizontal Line Test to determine whether the following statement is true or false.
The function
is one-to-one on its entire domain and therefore has an inverse function.
The function

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19
Match the graph of the function given below with the graph of its inverse function.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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20
True or False: The function
is one-to-one on its entire domain.

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21
Evaluate the expression
without using a calculator.
A)
B)
C)3
D)5
E)4

A)

B)

C)3
D)5
E)4
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22
Find the domain and range of the function
.
A)domain:
Range:
B)domain:
Range:

C)domain:
Range:

D)domain:
Range:

E)domain:
Range:


A)domain:

Range:

B)domain:

Range:

C)domain:

Range:

D)domain:

Range:

E)domain:

Range:

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23
Evaluate (if possible)the function
at
.Simplify the result.
A)4
B)3
C)-3
D)5
E)undefined


A)4
B)3
C)-3
D)5
E)undefined
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24
Find the domain and range of the function
.
A)domain:
Range:

B)domain:
Range:

C)domain:
Range:

D)domain:
Range:

E)none of the above

A)domain:

Range:

B)domain:

Range:

C)domain:

Range:

D)domain:

Range:

E)none of the above
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25
Find
if
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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26
Let
.Then simplify the expression
.
A)6
B)5
C)10
D)2
E)undefined


A)6
B)5
C)10
D)2
E)undefined
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27
You need 50 pounds of two commodities costing $1.55 and $2 per pound.Find the inverse function of the cost function
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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28
Use the functions
and
to find the function
.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

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29
Write the following expression in algebraic form.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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30
Solve the following equation for x.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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31
Let
.Evaluate the expression
and then simplify the result.
,
A)
B)
C)
D)
E)undefined




A)

B)

C)

D)

E)undefined
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32
Evaluate the expression
without using a calculator.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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33
Solve the following equation for x.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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34
Evaluate (if possible)the function
at
.Simplify the result.
A)
B)
C)
D)


A)

B)

C)

D)

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35
Evaluate the expression
without using a calculator.
A)0
B)
C)
D)
E)

A)0
B)

C)

D)

E)

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36
Use the functions
and
to find the function
.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

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Unlock for access to all 96 flashcards in this deck.
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37
Write the following expression in algebraic form.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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38
You need 50 pounds of two commodities costing $1.60 and $1.95 per pound.Determine the number of pounds of the less expensive commodity purchased if the total cost
is $94.
A)10 pounds
B)17 pounds
C)7 pounds
D)5 pounds
E)13 pounds

A)10 pounds
B)17 pounds
C)7 pounds
D)5 pounds
E)13 pounds
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39
Write the following expression in algebraic form.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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Unlock Deck
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40
Evaluate (if possible)the function
at
.Simplify the result.
A)9
B)-7
C)-11
D)13
E)undefined


A)9
B)-7
C)-11
D)13
E)undefined
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41
Specify a sequence of transformations for the function
that will yield the graph of h from the graph of the function
.
A)The function
is a horizontal shift
units to the right,followed by a vertical shift 6 units downwards.
B)The function
is a horizontal shift
units to the left,followed by a vertical shift 6 units upwards.
C)The function
is a horizontal shift
units to the left,followed by a horizontal shift 6 units to the right.
D)The function
is a vertical shift
units downwards,followed by a horizontal shift 6 units to the right.
E)The function
is a vertical shift
units upwards,followed by a horizontal shift 6 units to the left.


A)The function


B)The function


C)The function


D)The function


E)The function


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42
Determine whether the function is even,odd,or neither.
A)odd
B)even
C)neither

A)odd
B)even
C)neither
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43
Find the coordinates of a second point on the graph of a function f if the given point
is on the graph and the function is odd.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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44
Determine whether y is a function of x.
A)no
B)yes

A)no
B)yes
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45
Use the graph of
given below to find the graph of the function
. 
A)

B)

C)

D)

E)




A)

B)

C)

D)

E)

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46
Determine the domain and range of the function
.
A)domain:
Range:

B)domain:
Range:

C)domain:
Range:

D)domain:
Range:

E)domain:
Range:


A)domain:

Range:

B)domain:

Range:

C)domain:

Range:

D)domain:

Range:

E)domain:

Range:

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47
An open box of maximum volume is to be made from a square piece of material 4 centimeters on a side by cutting equal squares from the corners and turning up the sides(see figure).What is the domain of the function
.
A)domain:
B)domain: 4
C)domain:
D)domain:
E)domain: 2



A)domain:

B)domain: 4
C)domain:

D)domain:

E)domain: 2
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48
Determine whether y is a function of x.
y
A)no
B)yes

A)no
B)yes
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49
The horsepower H required to overcome wind drag on a certain automobile is approximated by
,
,where x is the speed of the car in miles per hour.Find
.Round the numerical values in your answer to five decimal places.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

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50
Given
and
,evaluate
.
A)0
B)
C)
D)-1
E)



A)0
B)

C)

D)-1
E)

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51
Find the slope of the line passing through the points
and
.
A)15
B)-5
C)
D)5
E)-


A)15
B)-5
C)

D)5
E)-

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52
Find the slope of the line passing through the pair of points.
,
A)
B)
C)
D)
E)0


A)

B)

C)

D)

E)0
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53
Find the domain and range of the function
.
A)domain:
Range:

B)domain:
Range:

C)domain:
Range:

D)domain:
Range:

E)domain:
Range:


A)domain:

Range:

B)domain:

Range:

C)domain:

Range:

D)domain:

Range:

E)domain:

Range:

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54
Find the coordinates of a second point on the graph of a function f if the given point
is on the graph and the function is even.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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55
An open box of maximum volume is to be made from a square piece of material 16 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure).Write the volume V as a function of x,the length of the corner squares.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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56
Evaluate the function
at
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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57
Determine whether the function is even,odd,or neither.
A)even
B)odd
C)neither

A)even
B)odd
C)neither
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58
Use the graph of
given below to find the graph of the function
.
A)

B)

C)

D)

E)




A)

B)

C)

D)

E)

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59
Sketch the line passing through the point
with the slope
.
A)

B)

C)

D)

E)



A)

B)

C)

D)

E)

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60
Estimate the slope of the line from the graph.
A)
B)5
C)2
D)
E)

A)

B)5
C)2
D)

E)

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61
Suppose that the dollar value of a product in 2008 is $150 and the rate at which the value of the product is expected to increase per year during the next 5 years is $4.5.Write a linear equation that gives the dollar value V of the product in terms of the year t.(Let
represent 2000. )Round the numerical values in your answer to one decimal place,where applicable.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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62
Find an equation of the line that passes through the points
and
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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63
Find an equation of the line through the points of intersection of
and
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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64
A company reimburses its sales representatives $145 per day for lodging and meals plus 42¢ per mile driven.Write a linear equation giving the daily cost C to the company in terms of x,the number of miles driven.Round the numerical values in your answer to two decimal places,where applicable.
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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65
Find an equation of the line that passes through the point
and has the slope
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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66
A real estate office handles an apartment complex with 50 units.When the rent is $700 per month,all 50 units are occupied.However,when the rent is $745,the average number of occupied units drops to 47.Assume that the relationship between the monthly rent p and the demand x is linear.Predict the number of units occupied if the rent is raised to $790.
A)41 units
B)56 units
C)59 units
D)47 units
E)44 units
A)41 units
B)56 units
C)59 units
D)47 units
E)44 units
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67
Find an equation of the line that passes through the points
and
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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68
A moving conveyor is built to rise 5 meters for every 12 meters of horizontal change.Find the slope of the conveyor.
A)0
B)
C)
D)
E)
A)0
B)

C)

D)

E)

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69
Find the y-intercept of the line
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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70
Find the slope of the line
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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Unlock Deck
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71
Use the result,"the line with intercepts
and
has the equation
,
,
",to write an equation of the line with x-intercept:
and y-intercept:
.
A)
B)
C)
D)
E)







A)

B)

C)

D)

E)

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72
Sketch a graph of the equation
.
A)

B)

C)

D)

E)


A)

B)

C)

D)

E)

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73
Write an equation of the line that passes through the point
and is parallel to the line
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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74
Find an equation of the line that passes through the point
and has the slope m that is undefined.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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75
If a line has slope
and passes through the point
,through which of the following points does the line also pass?
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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76
A moving conveyor is built to rise 1 meter for every 9 meters of horizontal change.Suppose the conveyor runs between two floors in a factory.Find the length of the conveyor if the vertical distance between floors is 10 meters.Round your answer to the nearest meter.
A)100 meters
B)79 meters
C)91 meters
D)90 meters
E)81 meters
A)100 meters
B)79 meters
C)91 meters
D)90 meters
E)81 meters
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77
Write an equation of the line that passes through the point
and is perpendicular to the line
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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78
Find the distance between the point
and line
using the formula,
for the distance between the point
and the line
.
A)
B)
C)
D)





A)

B)

C)

D)

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79
A company reimburses its sales representatives $155 per day for lodging and meals plus 40¢ per mile driven.How much does it cost the company if a sales representative drives 133 miles on a given day? Round your answer to the nearest cent.
A)217.00
B)208.20
C)134.33
D)156.33
E)186.20
A)217.00
B)208.20
C)134.33
D)156.33
E)186.20
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80
A real estate office handles an apartment complex with 50 units.When the rent is $680 per month,all 50 units are occupied.However,when the rent is $725,the average number of occupied units drops to 47.Assume that the relationship between the monthly rent p and the demand x is linear.Write a linear equation giving the demand x in terms of the rent p.
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

Unlock Deck
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