Deck 1: Functions Given by Formulas

Question 1

If represents the value of a car t years after it is purchased from the dealer, then indicates the value of the car on the showroom floor.

Answer 1

True

Question 2

If represents the cost of purchasing b burgers, f orders of fries, and d drinks, then represents 10 burgers, 6 orders of fries, and 12 drinks.

Answer 2

False

Question 3

The functional notation means the function whose name is evaluated at .

Answer 3

True

Question 4

If represents the cost of purchasing b belts, e pairs of earrings, and n necklaces, then we can use to indicate the cost of buying 2 belts, 4 pair of earrings, and 1 necklace.

Question 5

The only valid way of presenting a function is with a formula.

Question 6

The distance, in miles, from me to a moving train is given by . ​
Here t represents hours since I heard the train whistle.Calculate the distance to the train 5 hours after I heard the whistle.
​

A) 5 miles
B) 208.63 miles
C) 43525.00 miles
D) 147.56 miles

Question 7

If , calculate the value of . ​

A) 1.30
B) 3.07
C) 2.00
D) 2.19

Question 8

If , calculate the value of ​

A) -7.42
B) 13.32
C) -9.96
D) -5.66

Question 9

If , calculate the value of . ​

A) 112.01
B) 289.68
C) 111.37
D) -0.63

Question 10

If represents federal defense spending t years after 2000, then represents federal defense spending in 2012.

Question 11

For functions that model practical phenomena, the variables involved often have units associated with them.

Question 12

The functional notation means .

Question 13

If , calculate the value of . ​

A) 75.69
B) 93.09
C) 95.09
D) None of the above

Question 14

The number of electrical outlets needed in an office building depends on the number of offices and the number of employees.If there are f offices and e employees, then the number of outlets needed is ​ ​
Use functional notation to represent the number of outlets needed if there are 29.00 offices and 43.00 employees.Then calculate that value.Round your answer to the nearest whole number.
​

A) Functional notation: .Value: 93 outlets.
B) Functional notation: .Value: 98 outlets.
C) Functional notation: .Value: 123 outlets.
D) Functional notation: .Value: 75 outlets.

Question 15

If , calculate the value of . ​

A) 0.64
B) 1.00
C) 1.76
D) 4.07

Question 16

If , calculate the value of . ​

A) 5.55
B) 3.41
C) 1.66
D) 2.32

Question 17

If , calculate the value of ​

A) 2.93
B) 45.26
C) 4.04
D) None of the above

Question 18

If , calculate the value of .Round your answer to two decimal places if necessary. ​

A) 265.07
B) 2,379.73
C) 1,768.85
D) -1,768.85

Question 19

If , calculate the value of . ​

A) 185.27
B) 613.71
C) 187.82
D) 402.27

Question 20

If , calculate the value of . ​

A) -1.92
B) 1.23
C) -8.07
D) 12.65

Question 21

A water source is contaminated with a toxic chemical and is being cleaned.The amount of chemical, in grams, remaining t hours after the cleaning process began is given by ​ .
​
How much of the chemical is removed from time to time ?
​

A) 361.43 grams
B) 4.17 grams
C) 24.34 grams
D) 19.99 grams

Question 22

Let denote the traffic fine, in dollars, associated with driving m miles per hour over the speed limit.Explain in practical terms the meaning of .

Question 23

The balance of a savings account t months since it was opened depends on the APR.If the APR is A, expressed as a decimal, then the balance is given by . ​
What is the balance after 8.00 years if the APR is 6.00 percent? (Be sure first to express the APR as a decimal.)
​

A) $161923.43
B) $10198.15
C) $6575.19
D) None of the above

Question 24

A rock is tossed upward from the top of a building and allowed to fall to the ground.Its height above ground, in feet, t seconds after the toss is given by ​
How tall is the building?

Question 25

If represents the library charges on b books that are w weeks overdue, explain in practical terms the meaning of .

Question 26

For medium-sized dog breeds, the predicted adult weight, in pounds, of a puppy that weighs w pounds at age a weeks is given by the function ​ .
​
Use functional notation to express the predicted weight of a puppy that weighs 3.00 pounds at age 7 weeks.Then calculate that value.
​

A) Functional notation: .Value is 22.29 pounds.
B) Functional notation: .Value is 121.33 pounds.
C) Functional notation: .Value is 7 pounds.
D) None of the above.

Question 27

The number of armadillos in a certain area t years since observation began is given by ​ ​
How much did the armadillo population grow from year 2.00 to year 7.00? Round your answer to the nearest whole number.
​

A) 0
B) 854
C) 218
D) 1071

Question 28

Let denote the price in dollars of p pizzas, s sodas, and c bags of chips.Use functional notation to indicate the cost of 5 pizzas, 4 sodas, and 4 bags of chips.

Question 29

In the event of an emergency stop, the speed S, in miles per hour, of a car when brakes are applied can be calculated from the length L, in feet, of skid marks.The relationship is .Suppose skid marks are 67.40 feet long.Use functional notation to express the speed of the car, and then calculate that value. ​

A) miles per hour
B) miles per hour
C) miles per hour
D) miles per hour

Question 30

A desalination process is removing salt from a container of sea water.The amount of salt, in kilograms, remaining t hours after the cleaning process began is given by ​ .
​
How much of the salt is removed from time to time ?
​

A) 5.73 kilograms
B) 4.17 kilograms
C) 9.70 kilograms
D) 6.02 kilograms

Question 31

Let denote the monthly payment if you borrow P dollars at an APR of A percent, and the loan is repaid in t months.Use functional notation to indicate the monthly payment if you borrow 5532 dollars at an APR of 4.22 percent, and you repay the loan in 4 years.

Question 32

Let denote the temperature of an oven t minutes after it is turned on.Use functional notation to indicate the temperature of the oven one hour and 48 minutes after it is turned on.

Question 33

A rock is tossed upward from the top of a building and allowed to fall to the ground.Its height, in feet, above the ground after t seconds is given by ​ .
​
Use functional notation to express the height of the rock after 0.44 seconds.Then calculate that value.
​

A) Functional notation .Value is 74.50 feet.
B) Functional notation .Value is feet.
C) Functional notation .Value is 60.70 feet.
D) None of the above.

Question 34

The height H, in feet, of the winning pole value in the early years of the Olympic games can be modeled by ​ ​
Where t is years since 1900.Use functional notation to express what the height of the winning pole vault would have been in 1928.00.Then calculate that value.
​

A) Functional notation: .Value is 303.40 feet.
B) Functional notation: .Value is 20880.40 feet.
C) Functional notation: .Value is 15.31 feet.
D) Functional notation: .Value is 319.31 feet.

Question 35

If represents the library charges on b books that are w weeks overdue, explain in practical terms the meaning of .

Question 36

If you are driving at a speed of S miles per hour and make an emergency stop, you can expect to leave skid marks of length L feet.The relationship is ​ ​
Suppose your speed is 82.00 miles per hour.Use functional notation to express the length of skid marks an emergency stop will produce, and then calculate that value.
​

A) feet
B) feet
C) feet
D) feet

Question 37

Let denote the balance, in dollars, of an account t months after the account is opened.Use functional notation to indicate the balance of the account after 2 years and 11 months.

Question 38

Let denote the monthly payment if you borrow P dollars at a monthly rate of r expressed as a decimal, and the loan is repaid in t months.Use functional notation to indicate the monthly payment if you borrow 5726 dollars at an APR of 9.44 percent, and you repay the loan in 5 years.Use 3 decimal places for r.