Lesson 9

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?

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 $A(n)=93.5\left(\frac12\right)^n$.

   

   

   $n$	$A$

 

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