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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