Here are descriptions of relationships between quantities. For each description:

• Make a table of at least 5 pairs of values that represent the relationship.
• Plot the points. Label the axes of the graph.

• Answer these questions and explain your reasoning: Should the points be connected? Are there any input or output values that don’t make sense? 

1. A cab charges $1.50 per mile plus $3.50 for entering the cab. The cost of the ride is a function of the miles ridden , and is defined by .

   

2. The admission to the state park is $5.00 per vehicle plus $1.50 per passenger. The total admission for one vehicle is a function of the number of passengers , defined by the equation .

   

3. A new species of mice is introduced to an island, and the number of mice is a function of the time in months  since they were introduced. The number of mice is represented by the model .

   

4. When you fold a piece of paper in half, the visible area of the paper gets halved. The area is a function of the number of folds , and is defined by .

   

To make sense in a given context, many functions need restrictions on the domain and range. For each description of a function:

• Describe the domain and range.
• Describe what its graph would look like (separate dots or connected).

1. weight of a puppy as a function of time

2. number of winter coats sold in a store as a function of temperature outside

3. number of books in a library as a function of number of people who live in the community the library serves

4. height of water in a tank as a function of volume of water in the tank

5. amount of oxygen in the atmosphere as a function of elevation above or below sea level

6. thickness of a folded piece of paper as a function of number of folds