Sec 1.1 Functions and Change
Def. A function is a rule that takes certain numbers as
inputs and assigns to each a definite
output number.
The set of all input numbers is
called the Domain of the
function.
The set of all output numbers is
called the Range of the
function.
The input is called the independent variable. ( often x or t
)
The output is called the dependent variable. ( often y, f(x), or f(t) )
Some quantities are discrete: they can only take on
certain isolated values.
Ex. dates, number of units sold,
number of people present can only be represented by (non-negative) integers.
Other quantities are continuous: they can take on any
values.
Ex. height, time, temperature…
Notation:
set of all numbers t such that 
notated as 
set of all numbers t such that 
notated as 
Table
|
Month |
jan |
feb |
mar |
april |
may |
june |
july |
aug |
sept |
oct |
nov |
dec |
|
avg. precip. in inches |
2.18 |
1.97 |
1.94 |
1.71 |
1.62 |
1.09 |
0.54 |
0.78 |
0.98 |
1.55 |
2.65 |
2.52 |
Data from
Domain:
Range:
Graphs
Words: Eduard has to travel 30 miles to the nearest post office.
Gas costs $3.489/gallon and his car
gets 27 mpg.
Stamps cost $0.43 each.
a) Find the following linear function: cost of mailing letters as a function of
numbers of letters to be sent.
b. Find the family of linear
functions for varying prices of gas and stamps.
Language:
Function f is increasing is values
of f(x) increase as x
increases.
(rising left to right)
Function f is decreasing is values
of f(x) decrease as x
increases. (falling left to right)
y is proportional to x if there exists a 
such that 
y is inversely proportional to x if there exists a such that 
ex. The circumference of a circle is
proportional to the radius of the circle.
ex. The area of a circle is
proportional to the square of the radius of the circle.
Conceptual Problem:
Terry leaves home to drive to a store
15 miles away.
At a distance of 10 miles from home
Terry receives a call, pulls the car over to talk, and then starts back toward
home.
After going 2 miles, Terry receives
another call, pulls over to talk, and then once the conversation is over heads
back toward the store, eventually getting there and parking in the lot.
a) Draw a graph of distance from home
as a function of time for the story.
b) Draw a graph of velocity as a
function of time for the story.
