Mathematical Curve Conjectures—Graphing Guide

To illustrate the student conjectures and the actual hyperbolic cosine, please use the Mathematics Visualization Toolkit (MVT) (http://amath.colorado.edu/java/) and take the following steps:

•	Open the MVT software (you may run this directly on their server or download it to your personal computer and run it from there)
•	Use the access path:  Tools/Graphing Tools/Function Plotter

When the Function Plotter opens, 

•	Click on Show Options
•	Click on Domain/Range Options if necessary for access

To display the curves f(x)=x^2+1 and f(x)=cosh(x) on the same set of axes

•	Click the Overlay checkbox (so that you can graph two functions on the same axes)
•	Enter x^2+1 in the f(x) textbox
•	Enter x: from -4 to 4 in the Independent Variable area
•	Uncheck the checkbox for Use Defaults in the Dependent Variable area
•	Enter f(x): from 0 to 20 in the Dependent Variable area
•	Click on Plot
•	Enter cosh(x) in the f(x) textbox
•	Click on the tab labeled Appearance Options
•	Select the Line Color red from the dropdown list
•	Click on Plot
•	Click on Hide Tools to obtain a full-width view of the graphs

Note the differences and similarities in the two graphs: the hyperbolic cosine is flatter near the origin and then rises more rapidly than the quadratic curve; both curves are symmetric with respect to the y-axis and intersect at just less than 3 units from the origin.