- 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.
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 \(c(m)=1.50m+3.50\).
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 \(a(p) = 5 + 1.50p\).
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 \(b(t)=16 \boldcdot (1.5)^t\).
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 \(A(n)=93.5\left(\frac12\right)^n\).
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