Transcript The Fibonacci Function

My Three Functions
By David Bishop
The Square Root Function
f ( x)  x
x
f(x)
0
1
2
3
4
5
6
7
8
9
10
0
1
1.414213562
1.732050808
2
2.236067977
2.449489743
2.645751311
2.828427125
3
3.16227766
Used http://rechneronline.de/function-graphs/
to get the graph.
The Square Root Function
Variables

x is the independent
variable
◦ x determines the output
of the square root
function.

f(x) or y is the
dependent variable
◦ We need to know what x
is before we can know
f(x) or y.
Domain and range

Domain
◦ All nonnegative real
numbers

Range
◦ All nonnegative real
numbers
f ( x)  x
The Square Root Function
The Fibonacci Function
The Fibonacci Sequence
•A series of numbers that start with 0,1
•The next number in the series is
always determined by the sum of the
previous two numbers
The Fibonacci Function
•Returns the nth number of the
Fibonacci Sequence
Fn
Leonardo Pisano Bigollo
(Fibonacci)
The Fibonacci Function
Picture and equation from
http://www.fibonacci.nam
e/
Variables


n is the independent
variable
F(n), the Fibonacci
number, is the
dependent variable
◦ We need to know what n
is in order to know what
Fibonacci number to
obtain.
Domain and range

Domain
◦ All nonnegative integers

Range
◦ The numbers of the
Fibonacci sequence:
 0,1,1,2,3,5,8,13…
Fn
The Fibonacci Function
F(n)
0
1
2
3
4
5
6
7
8
9
10
0
1
1
2
3
5
8
13
21
34
55
Fibonacci Function
60
50
40
F(n)
n
30
20
10
0
0
2
4
6
8
n
The Fibonacci Function
10
12
Some Uses of the
Fibonacci Function
•Primarily used in a branch of
mathematics known as Number
Theory
•The financial world uses Fibonacci
numbers to study trends in the
market.
•Some patterns in nature have
been found to be connected to
the Fibonacci sequence
The Fibonacci Function
The Visitors Function
Hoping For Something To Hope For
•An amateur blog
•Subjects covered include movies, music, and
television
•Established in January 2008
•Member #149 of the Large Association of
Movie Blogs
The Visitors Function
Hoping For Something To
Hope For
• A record has been made of the
number of visitors to the blog
each day.
•We can plot the total number of
visitors for each month.
The Visitors Function
Variables


Time is the
independent variable
The number of
visitors is the
dependent variable
Domain and Range

Domain
◦ All months that the
website is/was online.

Range
◦ Almost all nonnegative
integers
 Limited by population
and days in a month
The Visitors Function
Visitors per
Visitors
Month
per(with
Month
trendline)
3000
Number of visitors
2500
2000
1500
1000
500
0
Jun-08
Sep-08
Dec-08
Mar-09
Jul-09
Jul-09
Oct-09
Oct-09
Jan-10
Jan-10
Month
Month
The Visitors Function
May-10
May-10
Aug-10
Aug-10
Nov-10
Nov-10