Deck 1: Data, Functions, and Models

Question 1

If the temperatures over a 12-hour period in Phoenix, Arizona were 76, 81, 90, 98, 101, 106, 100, 98, 93, 83, 72, and 75, what was the median temperature during this time period?

A) 90
B) 100
C) 106
D) 93
E) 91.5

Answer 1

91.5

Question 2

The set of all possible inputs is called the domain of the function.

Answer 2

True

Question 3

All functions can be represented verbally, symbolically, numerically, and graphically.

Answer 3

False

Question 4

The price per gallon of gas at various gas stations around town is listed in the table below. What is the median price per gallon? (Rounded to the nearest hundredth)

A) $2.88
B) $2.78
C) $3.02
D) $2.42
E) $2.56

Question 5

A variable y is a function of a variable x if each value of x (the input) corresponds to exactly one value of y (the output).

Question 6

If the temperatures over a 12-hour period in Phoenix, Arizona were 72, 83, 91, 90, 103, 102, 98, 96, 93, 82, 80, and 72, what was the average temperature during this time period? (Round to the nearest degree)

A) 91
B) 72
C) 96
D) 89
E) 1062

Question 7

The table below gives the cost for one-credit of tuition at various colleges.

The median cost gives a better description than average cost for the tuition costs.

Question 8

If the net change of a function f from a to b is negative, then the function must steadily increase from a to b .

Question 9

The table below illustrates a set of data for a function.

Question 10

The graph of f(x) = -8 is a horizontal line.

Question 11

All relations are functions.

Question 12

A table of values is an example of a numeric representation of a function.

Question 13

The table below illustrates a set of data for a function.

Question 14

If your quiz scores for MAT 101 are 85, 92, 75, 100, and 69, what is your quiz average?

A) 421
B) 84.2
C) 4.21
D) 75
E) 105.25

Question 15

The table below describes the average temperatures for Portland, OR during a given year. What is the average temperature for the year? (Rounded to the nearest tenth)

A) 61.0
B) 68.5
C) 70.0
D) 67.0
E) 63.1

Question 16

The table below describes the average temperatures for Portland, OR during a given year. What is the median temperature for the year?

A) 64.5
B) 67.0
C) 75.0
D) 71.0
E) 64.0

Question 17

The relation is not a function.

Question 18

The price per gallon of gas at various gas stations around town is listed in the table below. What is the average price per gallon? (Rounded to the nearest hundredth)

A) $2.31
B) $2.52
C) $2.82
D) $2.76
E) $3.02

Question 19

If the net change of a function f from a to b is zero, then the function must be constant between a and b .

Question 20

All functions are relations.

Question 21

Find the input(s) corresponding to the output of 30.

A) 30 and 35
B) 7 and 31
C) 7
D) 31
E) 35

Question 22

Find the output(s) corresponding to the input of 30.

A) 10
B) 0
C) 30
D) 5
E) 55

Question 23

The cost for a cell phone plan starts at $29.99 per month plus $0.07 per minute. Which of the following models the monthly cost of the cell phone based on the number of minutes used?

A) C = 29.99 m
B) C = 0.07 + 29.99 m
C) C = 29.99 + 0.07 m
D) C = 0.07 m
E) C = 29.99 0.07 m

Question 24

For the scatter plot below, which statement describes the relationship between the variables?

A) As the time increases, the temperature increases.
B) As the time increases, the temperature decreases.
C) As the time decreases, the temperature stays constant.
D) There is no relationship between the variables.
E) As the time decreases, the temperature decreases.

Question 25

Using the table below, determine the value for the blank.

A) -6
B) -3
C) -13
D) -2
E) 14

Question 26

The following table shows the values of airfare for a roundtrip ticket from San Antonio, TX to Portland, OR.

Which one of the following scatterplots illustrates this data?

A)
B)
C)
D) None of these options.
E)

Question 27

The number of gallons of water remaining in a pool t hours after it began to drain is illustrated in the table below.

What is the first difference of the number of gallons of water?

A) -2121
B) 2121
C) 424.2
D) -424.2
E) 5

Question 28

The number of gallons of water remaining in a pool t hours after it began to drain is illustrated in the table below.

What is the initial number of gallons of water in the pool before it began to drain?

A) 19500
B) 22000
C) 14500
D) 17000
E) 12000

Question 29

Which one of the following models the data graphed in the scatter plot.

A)
B)
C)
D)
E)

Question 30

Find the domain and range of the relation .

A) Domain: ; Range:
B) Domain: ; Range:
C) Domain: ; Range:
D) Domain: ; Range:
E) Domain: ; Range:

Question 31

The table below describes the average temperatures for Portland, OR during a given year. What month had the lowest temperature?

A) January
B) November
C) March
D) February
E) December

Question 32

The mass of bacteria (in micrograms) in a Petri dish for different times is shown in the table below. Approximately what time was the mass of the bacteria 45 mcg?

A) Between 9:00 am and 9:30 am
B) Between 9:30 am and 10:00 am
C) Not enough information
D) Between 8:30 am and 9:00 am
E) Between 8:00 am and 8:30 am

Question 33

The value V of a historic vehicle can be modeled by V = 52500 + 2075 t where t represents the age of the vehicle above 35 years. What is the value of the vehicle when it is 50 years old?

A) $52500
B) $125125
C) $83625
D) $156250
E) $21375

Question 34

The table below describes the average temperatures for Portland, OR during a given year. What was the average temperature for May?

A) 73
B) 81
C) 68
D) 42
E) 60

Question 35

The mass of bacteria (in micrograms) in a Petri dish for different times is shown in the table below. What is the mass of the bacteria (in mcg) at 9:30 am?

A) 61.89
B) 75.79
C) 50.60
D) 1.5
E) 31.08

Question 36

The mass of bacteria (in micrograms) in a Petri dish for different times is shown in the table below. By how much did the bacteria grow from 8:30 am to 10:30 am?

A) 73.18
B) 51.35
C) 38.80
D) 34.38
E) 2

Question 37

Given the data below, how can you determine if the set of data has a linear model?

A) By verifying that the salary values increases when the number of years increases.
B) Not enough information
C) By verifying that the first differences of the salary values are constant for successive increases in the number of years.
D) By verifying that the salary increases by the same amount.
E) By verifying that the number of years increases by the same amount.

Question 38

The following table shows data for the cost of humidifiers based on the number of humidifiers produced. Find a linear model for the cost C of producing x humidifiers.

A) C = 1.05 + 87 x
B) C = 1.05 x
C) C = 87 + 1.05 x
D) C = 87 + 20 x
E) C = 87 x

Question 39

The number of gallons of water remaining in a pool t hours after it began to drain is illustrated in the table below.

Which one of the following models this data?

A) N = 1750 350 t
B) N = 22500 + 1750 t
C) N = 22500 + 350 t
D) N = 22500 350 t
E) N = 22500 1750 t

Question 40

Using the table below, determine the value for the blank.

A) 24
B) 21
C) 28
D) 23
E) 27

Question 41

Which one of the following graphs represent the function:

A)
B)
C) None of these options.
D)
E)

Question 42

A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by h(t) = 16 t + 48 t + 111. What is the meaning of h (2)?

A) After 2 seconds, the height of the ball is 175 feet above ground.
B) After 2 seconds, the height of the ball is 143 feet above ground.
C) After 2 seconds, the height of the ball is 111 feet above ground.
D) After 2 seconds, the height of the ball is 32 feet above ground.
E) After 2 seconds, the height of the ball is 817 feet above ground.

Question 43

Given the table below, find the net change in the variable y as x changes from 2 to 4?

A) -9
B) 2
C) 9
D) 6
E) -3

Question 44

A population of rabbits was tracked over a 55-day period. The data is shown in the following graph. What was the maximum number of rabbits during this time period?

A) 61
B) 49
C) 38
D) 15
E) 83

Question 45

Consider the function f(x) = 4 x 7. What is the name of the function? What is the input? What is the output?

A) Name: f ; Input: x ; Output: 4 x 7
B) Name: f(x) ; Input: x ; Output: 4 x 7
C) Name: f(x) ; Input: 4 x 7; Output: x
D) Name: f(x) ; Input: x ; Output: f
E) Name: f ; Input: 4 x 7; Output: x

Question 46

Find the domain of .

A)
B)
C)
D)
E)

Question 47

A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by h(t) = 16 t + 48 t + 111. Find the net change in the height of the ball from time t = 1 seconds to t = 4 seconds.

A) 96 feet
B) 47 feet
C) -143 feet
D) -96 feet
E) 3 feet

Question 48

Determine the domain and range of the function represented by the graph.

A) Domain: ; Range:
B) Domain: ; Range:
C) Domain: ; Range:
D) Domain: ; Range:
E) Domain: ; Range:

Question 49

Let f(x) = 3 x + 4 x 4. Find f ( 4).

A) 48
B) -32
C) 32
D) 28
E) -68

Question 50

The temperature (in ° F) of a town is taken at the beginning of each hour throughout one day starting at 5 a.m. Let T be the function defined by T(x) = temperature of the town at time x . Which one of the following graphs represents this scenario?

A)
B) Not enough information
C)
D)
E)

Question 51

Use the following graph to create an algebra model for the function.

A)
B)
C)
D)
E)

Question 52

Which one of the following best describes the function ?

A) The rule h is "divide the input by 4 and subtract 1, then multiply by 6."
B) The rule h is "multiply the input by 6 and subtract 1, then divide by 4."
C) The rule h is "multiply the input by 6 and divide by 4, then subtract 1."
D) The rule h is "divide 6 by 4 and multiply by the input, then subtract 1."
E) The rule h is "subtract 1 from the input and multiply by 6, then divide by 4."

Question 53

A membership to a local fitness club costs $29 per month. The membership includes 10 hours of use of the club. If you want to use the club more than 10 hours per month, it will cost an additional $1.55 per hour. Which of the following functions model this situation?

A)
B)
C)
D)
E)

Question 54

A population of rabbits was tracked over a 55-day period. The data is shown in the following graph. How did the population of rabbits change between day 3 and day 20?

A) The population of rabbits increased from approximately 5 rabbits to 83 rabbits.
B) The population of rabbits decreased from approximately 83 rabbits to 5 rabbits.
C) The population of rabbits increased from approximately 5 rabbits to 61 rabbits.
D) The population of rabbits was constant during this time period.
E) The population of rabbits decreased from approximately 61 rabbits to 5 rabbits.

Question 55

A membership to a local fitness club costs $49 per month. The membership includes 20 hours of use of the club. If you want to use the club more than 20 hours per month, it will cost an additional $1.80 per hour. Let C represent the cost of the membership and x represent the number of hours of use of the club. Find and interpret .

A) The cost of 33 hours of use of the club per month is $49.00.
B) The cost of 33 hours of use of the club per month is $50.80.
C) The cost of 33 hours of use of the club per month is $108.40.
D) The cost of 33 hours of use of the club per month is $23.40.
E) The cost of 33 hours of use of the club per month is $72.40.

Question 56

The distance d (in miles) that a car travels based on the amount of time t (in seconds) is given by the equation d = 3 t 2 t . What is the net change in distance d when the time t changes from 0 to 2 seconds?

A) 8 miles
B) 12 miles
C) 0 miles
D) 2 miles
E) 36 miles

Question 57

The cost of college tuition for 12 credit hours at a local college during 2000 to 2008 is shown in the table below. Find the net change in the cost of college tuition from 2000 to 2005 and state if the net change was an increase or decrease.

A) -195, decrease
B) 312, increase
C) -312, decrease
D) 195, increase
E) 39, increase

Question 58

The verbal description below can be represented algebraically by which one of the following equations?
"To find the sales tax, take 7.5% of the purchase price."

A) y = 7.5 x, where y represents the sales tax and x represents the purchase price.
B) x = 0.075 y, where x represents the sales tax and y represents the purchase price.
C) y = 0.075 + x , where y represents the sales tax and x represents the purchase price.
D) y = 0.075 x, where y represents the sales tax and x represents the purchase price.
E) y = 7.5 + x, where y represents the sales tax and x represents the purchase price.

Question 59

Which one of the following represents the graph of ?

A)
B)
C)
D)
E) None of the above

Question 60

Given the table below, find the net change in the variable y as x changes from 1 to 4?

A) 8
B) 7
C) 6
D) 9
E) 0

Question 61

Find a function that models the volume V of a box with height x , length 6 x and width x + 8.

A) V(x) = (6 x )( x + 8)
B) V(x) = ( x + 6 x ) ( x + 8)
C) V(x) = x (6 x + x + 8)
D) V(x) = x (6 x )( x + 8)
E) V(x) = x + (6 x ) + ( x + 8)

Question 62

Find a function that models the area A of a rectangle whose length is 9 ft more than twice its width x .

A) A(x) = x (9 + 2 x )
B) A(x) = x (9 x + 2)
C) A(x) = (9 + 2) x
D) A(x) = x (9 + x )
E) A(x) = 9 + 2 x

Question 63

For the function , find the local maximum value of f .

A) 1.6
B) -0.6
C) 0
D) 1
E) 0.25

Question 64

For the function , find the intervals on which is increasing.

A)
B)
C)
D)
E)

Question 65

Which of the following formulas express the average score for 4 exams?

A)
B)
C)
D)
E)

Question 66

The table below shows the salary values for a job based on the number of years x worked. Find a linear model for the salary value S(x) as a function of the number of years x worked.

A) S(x) = 3000 x
B) S(x) = 36000 + 1000 x
C) S(x) = 1000 x
D) S(x) = 36000 + 3000 x
E) S(x) = 33000 + 1000 x

Question 67

Does the equation 3 x - 5 y = 4 define the variable y as a function of the variable x ?

Question 68

A population of rabbits was tracked over a 55-day period. The data is shown in the following graph. What was the approximate number of rabbits on day 30?

A) 40
B) 15
C) 10
D) 30
E) 83

Question 69

Solve the equation for .

A)
B)
C)
D)
E)

Question 70

The amount of an investment A after 36 months can be modeled by the formula where P is the initial investment amount and r % is the interest rate. If Marcus invests $2000 in this account with an interest rate of 3.7500%, how much money will be in the account at the end of 36 months? (Rounded to the nearest hundredths)

A) $7,526.65
B) $2,006.25
C) $2000
D) $72,225.00
E) $2,237.75

Question 71

The graphs of and are shown below. Find the value(s) of x for which .

A) -2.4 and 0.8
B) 0.8
C) -2.4 and -11.7
D) -2.4
E) -11.7 and 1.3

Question 72

Does the equation x = ( y 6) + 3 define the variable y as a function of the variable x ?

Question 73

Given the table below, is the variable y a function of the variable x ?

Question 74

A membership to a local fitness club costs $59 per month plus $1.15 for each hour spent in the club. Find a linear model for the monthly cost of membership C(x) as a function of the number of hours x spent in the club.

A) C(x) = 59 x + 1.15
B) C(x) = 1.15 x
C) C(x) = 59 x
D) C(x) = 59 + 1.15 x
E) C(x) = (59 + 1.15 )x

Question 75

Given the table below, is the variable y a function of the variable x ?

Question 76

The graphs of and are shown below. Find the value(s) of x for which .

A)
B)
C)
D)
E)

Question 77

For the function , find the local minimum value of f .

A) -0.6
B) -0.185
C) -1
D) 1
E) 1.6

Question 78

A population of rabbits was tracked over a 55-day period. The data is shown in the following graph. What was the minimum number of rabbits during this time?

A) 20
B) 37
C) 83
D) 5
E) 15

Question 79

The resistance R of a wire (in ohms) is related to its length L (in meters) and its diameter d (in meters) by the formula . Find a formula for d .

A)
B)
C)
D)
E)

Question 80

Find a formula that models the speed s of a car that travels d miles in t minutes.

A)
B)
C)
D)
E)