Domain/Range Word Problems

A plane can carry a maximum cargo weight of 160,000 pounds. A company uses one of these planes to ship 2,000-pound containers. The total cargo weight is a function of the number of containers in the plane. What is the greatest value in the domain for this situation?

• 2,000

• 80

• 320,000,000

• 160,000

The total cost in dollars to buy uniforms for the players on a volleyball team can be found using the function c = 34.95u + 6.25 where u is the number of uniforms bought. If there are at least 8 players but not more than 12 players on the volleyball team, what is the domain of the function for this situation?

• 0 < u $\le$ 12

• 0 < c $\le$ 425.65

• {285.85, 320.80, 355.75, 390.70, 425.65}

• {8, 9, 10, 11, 12}

A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by

f(x) = 20x + 4.

What is the range of the function for this situation?

• {0, 1, 2, 3, 4, 5, 6}

• {4, 24, 44, 64, 84, 104, 124}

• {0, 2, 4, 6}

• {4, 44, 84, 124}

The daily cost of hiring a plumber, y, to work x hours on a repair project can be modeled using a linear function. The plumber charges a fixed cost of $80 plus an additional cost of $45 per hour. The plumber works a maximum of 8 hours per day.

For one day of work, what is the range of the function for this situation?

• 0 $\le$ x $\le$ 8

• 80 $\le$ y $\le$ 440

• 0 $\le$ x $\le$ 10

• 45 $\le$ y $\le$ 685

A student jogged at a constant rate of 7 miles per hour for  $\frac{1}{3}$  hour. The function d = 7t can be used to find the distance in miles the student jogged during t, the time in hours. 
What is the range of the function for this situation? 

• 0 $\le$  t  $\le$   $\frac{1}{3}$  

• {0,  $\frac{7}{3}$  }

• 0  $\le$  d  $\le$   $\frac{7}{3}$  

• {0,  $\frac{1}{3}$  }

Customers can download books from an online bookstore for $8 each after paying $150 for an e-book reader. The total amount of money a customer spends on x books and the e-book reader can be found using f(x) = 8x + 150.

What is the range of f in this situation?

• {150, 158, 166, 174, …}

• {158, 159, 160, 161, …}

• All integers greater than or equal to 0.

• All real numbers greater than or equal to 150.

The cost to rent a mid-size SUV is $71 per day for up to 3 days. The function f(x) = 71x can be used to find the total cost of the rental, in dollars, based on x number of days it is rented. Which statement best fits the situation.

• A reasonable domain is x $\ge$ 0, since the data set is continuous and restricted to positive values only.

• A reasonable domain is all whole numbers, since the data set is discrete and restricted to positive values only.

• A reasonable domain is 0 $\le$ x $\le$ 3, since the data set is continuous, but is restricted to positive values up to 3.

• A reasonable domain is {0, 1, 2, 3}, since the data set is discrete and restricted to a maximum value of 3.