[list][*]Use the input boxes for [math]f(x)[/math] and [math]g(x)[/math] to define the two functions you want to combine. [/*][*]Adjust the slider tools for [math]a[/math] and [math]b[/math] to stretch/shrink or reflect the graphs of [math]f[/math] and [math]g[/math] individually. [/*][*]Use the slider tool "Combine f and g" to change the operation used to combine [math]f(x)[/math] and [math]g(x)[/math] to define a new function [math]h(x)[/math]. There are four options: addition, subtraction, multiplication, and division. [/*][/list]

Many real world relationships are too complex to describe with a single function formula. Two (or more) functions can be combined through the usual arithmetic operations (addition, subtraction, multiplication, division) to create new functions with their own behavior that can better model a real world relationship.[br][br]The new function is created by combining the [b]outputs [/b]of two (or more) functions through the usual arithmetic operations. For example:[br][list][*]Addition: [math]h(x)=f(x)+g(x)[/math][/*][*]Subtraction: [math]h(x)=f(x)-g(x)[/math][/*][*]Multiplication: [math]h(x)=f(x)g(x)[/math] [/*][*]Division: [math]h(x)=\frac{f(x)}{g(x)}[/math], where [math]g(x)\ne0[/math]. [/*][/list]I've also included an extra operation, which is a special type of multiplication that is just a number times a function. We typically call this constant a [i]coefficient[/i]. The effect of this operation is to stretch the graph vertically. [br][list][*]Constant Multiple: [math]h(x)=af(x)[/math] for some constant [math]a[/math].[/*][/list]