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.
\(x\)  0  1  2  3  4  5  6 

\(y\)  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.

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 \(c(m)=1.50m+3.50\).
\(m\) \(c\) 
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 \(a(p) = 5 + 1.50p\).
\(p\) \(a\) 
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 \(b(t)=16 \boldcdot (1.5)^t\).
\(t\) \(b\) 
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?)
 weight of a puppy as a function of time
 number of winter coats sold in a store as a function of temperature outside
 number of books in a library as a function of number of people who live in the community the library serves
 height of water in a tank as a function of volume of water in the tank
 amount of oxygen in the atmosphere as a function of elevation above or below sea level
 thickness of a folded piece of paper as a function of number of folds