This applet will illustrate the composition of two functions, f(x) and g(x).[br][br]You can display two functions by using the show check box for each equation. The default equations are [math]f(x) = x^2[/math] and [math]g(x) = -2x[/math], you can enter equations of your choice by entering the function of x of your choice.[br][br]f(x) will graph in [color=#c51414]red[/color], and g(x) will graph in[color=#0a971e] green[/color]. The composition will be displayed as h(x) and will display in [color=#1551b5]blue[/color]. By clicking on the appropriate check box, you will be able to display each graph separately or together.[br][br]Prior to displaying the solution function h(x), use the point tool to locate points on the grid for h(x), i.e., read the y-values of f(x) and g(x), perform the arithmetic operation chosen, and plot the y-value of h(x). Select at least 5 points to illustrate the trace of h(x). If using a SMART or Promethean board have students find and plot the points. Hide f(x) and g(x) to allow users to determine a pattern before displaying f(x).

This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers with a worksheet to be complete for a grade.[br][br]See these functions for similar activities...[br] 1. [url=http://www.geogebratube.org/material/show/id/57693]Adding Functions[/url] h(x) = f(x) + g(x)[br] 2. [url=http://www.geogebratube.org/material/show/id/57694]Subtracting Functions[/url] h(x) = f(x) - g(x)[br] 3. [url=http://www.geogebratube.org/material/show/id/57697]Multiplying Functions[/url] h(x) = f(x) g(x)[br] 4. [url=http://www.geogebratube.org/material/show/id/57698]Dividing Functions[/url] h(x) = f(x) / g(x)[br] 5. [url=http://www.geogebratube.org/material/show/id/57699]Composition of Functions[/url]: h(x) = f( g(x) )[br] 6. [url=http://www.geogebratube.org/student/m58005]Solving Rational Functions[/url]: f(x) = N(x)/D(x)