Lesson 9

Interpreting Functions

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.

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

$n$ $A$

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

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

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