# Domain and Range - Graphs and Word Problems (Grades 11-12)

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## Domain and Range - Graphs and Word Problems

1.

What is the domain of the function? Assume 1 unit intervals for both axes.

- All real numbers
- [math](-oo,0)[/math]
- [math] [0, +oo)[/math]
- [math](-oo, +oo)[/math]

2.

What is the domain and range of the graphed function?

- Domain and range are all real numbers.
- Domain is all real numbers less than zero and range is all real numbers.
- Domain is all real numbers and range is all real numbers equal to or less than zero.
- None of the above.

3.

What is the domain of the exponential function pictured below? Assume 1 unit intervals for both axes.

- [math]{x in RR | x > 0}[/math]
- [math]RR[/math]
- [math]{x in RR | x < 2}[/math]
- [math]{x in RR | x > -2 and x < 2}[/math]

4.

What is the range of the absolute value function pictured below? Assume 1 unit intervals for both axes.

- [math]RR[/math]
- [math]{y in RR | y !=0}[/math]
- [math]{y in RR | y >=0 }[/math]
- [math]{y in RR | y > 0}[/math]

5.

For the function pictured below, with endpoints at [math]x=0[/math] and [math]x=10[/math], what is the range of this function? Assume 1 unit intervals for both axes.

- [math]RR[/math]
- [math]{y in RR | y >= 0 and y <= 10}[/math]
- [math]{y in RR | y >= 0 and y <=4}[/math]
- [math]{y in RR | y >= 0}[/math]

6.

A bakery makes cookies and sells them for $2.00 each. The revenue the bakery makes from selling cookies is modeled by a function, where the input of the function is how many cookies the bakery makes. Which of the following would be the most appropriate domain for this function?

- The set of all integers.
- The set of positive integers and zero.
- The set of even numbers.
- The set of real numbers from 1 to 1,000.

7.

Shawn is filling a 5 L bottle with water. As the water increases, so does the weight of the bottle. This can be modeled by a function, where the input is how much water has been put into the barrel in liters. Which of the following would be the most appropriate domain for this function?

- The set of all real numbers.
- The set of integers numbers.
- The set of integers numbers, from 0 to 5.
- The set of all real numbers, from 0 to 5.

8.

A plane's fuel consumption depends upon the altitude it is flying at. If a plane is currently flying at 30,000 ft, a function can model how much its fuel consumption could improve or worsen by flying higher or lower than its current altitude. What would be the most appropriate domain for this function?

- [math]{x in RR | x <= 30","000}[/math]
- [math]{x in RR | x >= -30","000}[/math]
- [math]{x in RR | x >= -30","000 and x <= 15","000}[/math]
- [math]{x in RR | x >= 0 and x <= 30","000}[/math]

9.

Sarah is playing a game of cards, and she currently has 10 cards. The goal of the game is to get all the cards in the deck (which has 52 cards). Each turn every player has the ability to gain all the remaining cards in the deck, or to loose all their cards. If P(x) is a function that represents her probability of winning the game, where x is how many cards she either gains or looses in the next turn, which of the following would be the best domain for this function?

- [math]{x in ZZ | -10 <= x <= 42}[/math]
- [math]{x in ZZ | 0 <= x <= 52}[/math]
- [math]{x in ZZ | x >= 0}[/math]
- [math]{x in ZZ | x <= 52}[/math]

10.

Mia, who is a teacher, needs pencils for the upcoming school year, as she gives them out to students throughout the year. The pencils come in packages of 5, each package costing $2.00. The store only has 30 packages. If the function P(x) represents how many pencils Mia is able to buy with x dollars, what is the best domain for this function?

- [math]{x in RR | 0 <= x <= 60}[/math]
- [math]{x in RR | x >= 60}[/math]
- [math]{x in RR | 0 <= x <= 30}[/math]
- [math]RR[/math]

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