# Lesson 9

Interpreting Functions

• Let’s describe the domain of a function based on the context it models.

### 9.1: Notice and Wonder: What Do You See?

Here is a table of values of data that was collected.

 $$x$$ $$y$$ 0 1 2 3 4 5 6 6 5 4 3 2 1 0

Here are two graphs of the data. What do you notice? What do you wonder?

### 9.2: Connect . . . or Not

Here are descriptions of relationships between quantities.

• Make a table of at least 5 pairs of values that represent the relationship.
• Plot the points. Label the axes of the graph.
• Should the points be connected? Are there any input or output values that don’t make sense? Explain.

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, $$m$$, ridden and is defined by $$c(m)=1.50m+3.50$$.

$$m$$ $$c$$
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, $$p$$, defined by the equation $$a(p) = 5 + 1.50p$$.

$$p$$ $$a$$
3. A new species of mice is introduced to an island, and the number of mice is a function of the time in months, $$t$$, since they were introduced. The number of mice is represented by the model $$b(t)=16 \boldcdot (1.5)^t$$.

$$t$$ $$b$$
4. When you fold a piece of paper in half, the visible area of the paper gets halved. The area is a function of number of folds, $$n$$, and is defined by $$A(n)=93.5\left(\frac12\right)^n$$.

$$n$$ $$A$$

### 9.3: Thinking Like a Modeler

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