# xFunctions

### Welcome to xFunctions!

Please click on the button below to launch xFunctions in a separate window. Once it is open, feel free to enlarge the window to make it easier to view.

xFunctions has many different wonderful features. Feel free to explore it and learn what it can do! Some general instructions and other information about xFunctions can be found here.

## Graphing

When you first launch xFunctions, it begins at the Main Screen. For graphing purposes, select the 'Multigraph Utility' in the drop down menu at the top. This utility can be used to graph a function or several functions at once.

- Input the function in the box provided after "y= ".
For example, to enter the function 3x^{2}+p-e^{x+3}, you must type 3*x^2+pi-e^(x+3). Note the use of '*' for multiplication (Shift-8) and '^' for exponents (Shift-6). Parentheses are also important.
- Input your x and y ranges along the left side of the graphing window.
- Press the 'Graph!' button to plot the graph of the function.
- You can enter more functions by selecting a different function number just to the left of where you enter the function.
- Press the 'Graph!' button again, and you will get the graph of this function together with the previous function.

## Riemann Sums

When you first launch xFunctions, it begins at the Main Screen. For Riemann Sums, select the 'Riemann Sums Utility' in the drop down menu at the top. This utility computes Riemann sums for a specified function on a specified interval.

- Input the function in the box provided after "y= ".
For example, to enter the function 3x^{2}+p-e^{x+3}, you must type 3*x^2+pi-e^(x+3). Note the use of '*' for multiplication (Shift-8) and '^' for exponents (Shift-6). Parentheses are also important.
- Input the minimum and maximum x and y values in the boxes to the left side of the graph window.
- You can also input the number of subintervals you want to start with in the box labeled "Intervals".
- Hit the "Compute!" button.
- To get better area approximations, hitting the "Divide Intervals" button doubles the number of subintervals.

The values of various Riemann sums, using different rules, are shown to the right of the graph window. (The trapezoid rule isn't strictly a Riemann sum, but it's there as a choice anyway.) The area corresponding to **one** of the sums is displayed on the graph. Use the pop-up menu at the lower right to select which area is displayed. If you
click on the graph, you get details about one of the rectangles or trapezoids in the sum. (Click on the blue information box to get rid of it.) Note that for the "~Circumscribed" and "~Inscribed" rules, the maximum and minimum of the function on a sub-interval is only computed approximately.
(This explains the "~", which stands for "approximately.") Mouse zooming does **not** work on this screen.